Ole Gunnar Solskjaer's future at Old Trafford is far from secure and defeat at home to Arsenal on Monday night will pile more pressure on the Norwegian manager.
Likewise, Pochettino, who has been linked with the United job in the past, has endured a difficult season with Tottenham so far.
Spurs, who sit 10 points behind Liverpool in the Premier League, were knocked out of the Carabao Cup by League Two outfit Colchester United earlier in the week, with Pochettino claiming afterwards that some of his players had their own agenda.
Although Savage believes that the Argentine is the most attractive prospect for the Red Devils, the former Wales international suggests that neither club will be looking for a new manager before the end of this season - despite the 'smoke signals' that he's sending.
He wrote in The Mirror: "I know Spurs fans don’t like me saying this and I don’t like to because I have a soft spot for Tottenham. But Poch remains the most obvious candidate.
"I wonder if all these smoke signals he’s sending out – the messages that he’s feeling down, feeling flat – are essentially him saying to United: ‘Give me a shout, let’s talk, line up the move for the summer and in the meantime I will make sure I get Tottenham in the top four again’.
"Then we might see Solskjaer ousted at the end of the campaign. But, barring a complete disaster, it won’t be before then."
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