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After two finishes as runners-up behind Manchester City and Arsenal currently trailing Liverpool by 15 points this season, the Manchester United icon remains sceptical.
Speaking to Sky Sports after Arsenal's 1-1 draw with Manchester United, former midfielder Keane said: "No.
They've got close over the last few years, but City will be strong next year and I'm sure Liverpool will be too.
"Where is the evidence to think they can do it?
Will City and Liverpool just stand still.
They're going to look to improve, Pep will bounce back and I think Liverpool will be stronger next season.
"We don't know where Chelsea is, but what's the evidence or this group of players that they can do it.
Liverpool will be looking at that and not thinking they're going to be put under pressure, they'll be thinking Arsenal have almost given up the title chase.
"There's that striking issue, of course, but I still thought there would be that mentality of getting the job done.
On the one hand, you want to give some credit for the last few years but the next step is the hardest step."
Meanwhile, Arsenal manager Mikel Arteta was visibly upset after their draw with United, abruptly ending his post-match interview with Sky reporter Patrick Davison when questioned about Arsenal falling 15 points behind Liverpool in the title race this season.
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