Ronaldo has made it clear that he wants to leave United just a year after he returned to the club, but Old Trafford chiefs are reluctant to allow the 37-year-old to make his exit.
Speaking at a Sky Sports event in London, Keane suggested United need to find a solution to the Ronaldo problem, as he insisted last season’s top scorer needs to be integrated back into the squad.
"You have to try and keep Ronaldo because he's a brilliant player, but we don't know Ronaldo's behaviour when he's back in the building,” said Keane.
"I don't think it's as big of a deal as everyone's making out. When you're a manager, trouble comes your way, he has to deal with it.
"I think it can work out well for United. My worry is if he stays and United don't start great, and he's resentful to the manager, then it could get ugly.
"A lot of the issue is Ronaldo not playing in the Champions League for his ego, 'brand' or whatever.
"Why did his agent not have if Manchester United didn't get in the Champions League there's an option for both parties to have a look at it? If you've got this 'super agent' who has got unbelievable contacts and brilliant in terms of negotiations, why doesn't he have that in Ronaldo's contract?”
Keane went on to suggest Manchester City and Liverpool are the only two teams in contention to win the Premier League title, with Tottenham his dark horses to get in the mix at the top of the table.
“Liverpool and Man City are a level ahead of everyone else,” he continued. “We've seen that with recruitment. Even the game last week, I know it's only the Community Shield and pre-season, I just can't see the other teams getting near them for the title.
"There will be improvement at Tottenham and Manchester United have to be better than last year, but the simple answer in terms of winning the league: Liverpool and City. I can't see beyond it.
“Tottenham are the ones to watch. They've got two brilliant goalscorers if they stay fit then Spurs have a great chance in terms of doing better than Arsenal, Chelsea, United. I think Tottenham could do it.
"They've got a brilliant manager in (Antonio) Conte, they've got momentum into the club. Spurs can usually drag their heels during the summer but they've got their business done early. They've got decent strength in depth. Spurs could have a brilliant season. There's expectation now at the club. I've said before they ultimately always let you down. Can they back it up?”