The Red Devils have found themselves light on options up front this season after they allowed both Romelu Lukaku and Alexis Sanchez to leave the club in the summer.
Marcus Rashford has been leading the line for Manchester United in recent games, and Anthony Martial has only just recovered from an injury lay-off.
The January transfer window represents an opportunity for Solskjaer to bolster his squad for the second part of the campaign.
Spurs have been struggling to find consistent form so far this season and Manchester United legend Keane feels that the Red Devils should try and bring the 26-year-old striker to Old Trafford in January.
Speaking to Sky Sports after Sunday’s game, Keane said: “Just go and get Kane from Spurs, easy. Just go and get him. What are you all staring at?
“They’re in disarray, go and get him.”
Manchester United’s 1-1 draw with Liverpool FC on Sunday left them in 13th place in the Premier League table and just two points above the relegation zone.
The Red Devils will return to Premier League action with a trip to Norwich City on Sunday afternoon.
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