There have been signs of improvement and progression under manager Ole Gunnar Solskjaer in recent months and United are set to finish the campaign in second place, behind champions-elect Manchester City.
However, the Red Devils have not won the league title since Sir Alex Ferguson left the club in 2013 and Keane believes that they need to make a real statement of intent in the transfer market, suggesting a couple of Premier League stars they should look to target.
"They've got some brilliant players and I agree obviously that there's been progress. The next step for Man United is the biggest and the hardest one – and that is to go and get that league title.
"Liverpool were brilliant last year, Man City excellent this season but United are still a bit short, they've lacked that real bit of quality."
United spent around £75m on signings last summer, with their most notable addition being midfielder Donny van de Beek.