The Red Devils are in second place in the Premier League table and 16 points adrift runaway Premier League leaders Manchester City.
Manchester United are in a strong position to secure a top-four finish in Jose Mourinho’s second season in charge.
The 20-time English champions can win the FA Cup for the second time in three seasons but Manchester United will have to get past Tottenham Hotspur in the last four.
The Red Devils suffered a surprise 2-1 loss to La Liga side Sevilla in the Champions League round of 16 at Old Trafford earlier this month.
Manchester United have lacked depth in defence and in midfield this season following Eric Bailly’s injury problems and Paul Pogba’s struggles.
Former Red Devils star May believes Manchester United need at least four signings in the summer.
“I think we need another midfielder and a left-back would be sensible,” May told 888sport.
“Obviously Ashley Young is doing ever so well but it depends on what happens with Luke. We need another centre-half too and a centre-forward to put pressure on Lukaku.
“I think Lukaku is been outstanding to score better than one in two when he’s up there on his own. He should be pretty pleased with his season so far.”
Manchester United haven’t won the Premier League title since Sir Alex Ferguson’s retirement in 2013.
The Red Devils finished in sixth spot in the Premier League table in a disappointing top-flight campaign under Mourinho.
However, the Portuguese coach led Manchester United to Europa League and League Cup glory.
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