The former Red Devils captain was critical of the club's transfer policy during the past few seasons and says that they need to buy "big players" in order to succeed
David Moyes brought Marouane Fellaini to the club from Everton for a fee of £28 million (€33m) during the summer before signing Juan Mata from Chelsea for £37.1 million (€44m) in January.
However, despite such signings, former Red Devils captain Keane argues that the club is now feeling the effects of "cutting corners" in the transfer market over the previous few seasons.
"They've kind of cut corners in terms of transfers in the last few years, they've not gone out and got the big players, and it's just caught up with them this year," Keane told ITV.
"I think Man United need five or six players. If it happens in the summer then instead of being fearful of it, embrace it, it's exciting.
"These can be exciting times for Man United. Get them back to the very top where they belong."
After his side's 2-2 draw at home to Fulham on Sunday, Moyes has come under increasing pressure, but Keane, who is now Martin O'Neill's assistant manager with the Republic of Ireland national team, is adamant that Moyes requires more time to continue rebuilding the team.
"I think the man deserves plenty of time," said the Cork native of the former Everton boss.
"I think people have been afraid to use the word that there might be 'rebuilding' going on but that's exactly the word I would use."
Manchester United return to Champions League action on February 25 against Olympiacos and Keane dismissed suggestions that the season is over for David Moyes' men, stressing that there is always something to play for.
"You're playing for pride, you're playing for points," he said. "And United, if they do go out of the Champions League, still want to get in it next year.
"I think beating Olympiacos will be the priority. On form at this moment in time you have to say the Champions League is a long way off for Manchester United.
"But lots will change over the next few months," added Keane.