As a Man Utd fan I think United need potentially 2-3 first team players: CB, CDM, ST (433 formation). With about 4-5 players maybe needed for squad depth. Also there will be players leaving in the summer: Rooney, Young, Jones/Smalling, Darmian?, Fellaini and Blind.
There's still question marks over whether Zlatan will be at the club next season, a new ST is needed, from the looks of it, it won't be Griezmann this season but maybe next season? Potentially ST currently being looked at for Manchester United are Lukaku, Morata, Lacazette and Belotti. Very different sets of ST, but according to inside sources Mourinho is very high on Lukaku and Morata, as he has seen there developments of the past couple of seasons and has been very impressed with them. Will be interesting to see who goes to United. United will have quite a lot of competition for the ST as a host of clubs are wanting these 4. Lukaku a player Jose sold to Everton has his heart set on wanting to move to Chelsea, Morata who has also been linked to Chelsea and AC Milan, Lacazette who has been linked with Arsenal (but without Champions League football United are the front runners for his signature and finally Belotti are renowed ST fron Torino who has attracted attention from Chelsea, Manchester City, Juventus, AC Milan, Arsenal and Liverpool. Maybe Jose should look at other ST just incase.
Next position is CB, now Mourinho has been very impressed with Rojo and how he has turned out under his management. He obviously adores Bailly (as he did sign him) but he is not confident nor does he trust Smalling, Jones, Shaw, Darmian and Blind (with latter two linked with moves away) United will be bringing in a CB or two. Keane a former Man U player sold for £2M two years ago to Burnley tops the list of CB's interesting Jose with a £25M price tag after making his England debut and having a tremendous season with The Clarets this previous season, he would be definitely be more affordable than the other CB linked with moves to Old Trafford. Victor Lindelof is another CB from Benfica who Manchester United have been scouting since Jose arrived at Theater of Dreams also at the age of 22 could be a big player for the future but with a price tag £50M United could be looking elsewhere and final CB with concrete interest is former Celtic, now Southampton, Netherlands International Virgil Van Dijk probably the most sought defender in the Premier League in the summer transfer window also with a price tag similar to Lindelof, only difference besides age is he posses EPL experience and has a solid EPL season under his belt. With battles with Chelsea, Liverpool, Manchester City and Arsenal for his signature, money will surely talk for his signature (maybe barr the Gunners and Reds). Other CB that United have shown interest in are Marquinhos, Varane (very unlikely this move will happen as the player is happy at Real Madrid) and Eric Dier (also highly unlikely as Daniel Levy will not sell a player cheap).
Now the final position CM/CDM. With Carrick potentially playing his final season next season and the age of 36 as well is really making Mourinho think of a replacement in the last couple of months. Fellaini has been decent but not the ideal CM Jose wants. Now like I said earlier Eric Dier is a player he is looking at, He is also a player that he is a big admirer of and enjoys watching him play. Another player is Fabinho a RB who has been phenomenal at CM for Monaco and also capable of playing RB increases the interest from Jose but with teams like Manchester City and host of European Clubs fighting for his signature United need to vigorous and shrewd if they are to sign him. Another player is also a Monaco player known as Bakayoko, a CDM capable of playing CM again another player Manchester City, Chelsea and host of other clubs are tracking to sign also at the age of 22 its no surprise teams are looking at him.
Now a player who could be joining United is Ivan Perisic (a player who I would not sign for United what so ever) a Right footed LM who has been a subject of a £36M bid with Inter Milan wanting £48-£52M which is more than what United want to offer also at the ripe age of 28 its not a risk United want to take. But with this being said United and Perisic himself are very interested and hoping this deal goes through.
James Rodriguez is a CAM player who has been heavly linked with a move to United with reports suggesting a £42M bid had been accepted from Real Madrid, but from the past couple of weeks the interest has cooled down with Bayern Munich and Juventus front runners for the signature of the Colombian, but United still interetsed and James himself interested this move looks like it could increasing happen.
Now finally Manchester United recently got a offer of £60M for David De Gea from Real Madrid with United wasting no time in declining the offer and resolutely rejecting the offer. The understanding from the club is that Mourinho and the club don't want him go and the player is quite happy at United. Their's reports that United could be ready to offer the GK a new deal to keep him well away from Real Madrid. Also with Champions League football avaliable for United next season, the GK looks increasing to stay.