With just six months left on his current Gunners deal, Sanchez seemed destined to move to Manchester City in the January transfer window and reunite with manager Pep Guardiola.
United though, recently emerged as the front-runners as a move to Old Trafford seems imminent for the Chilean international at this stage.
However, the most recent development in the Sanchez saga is that Chelsea were reportedly ready to hijack a deal for the 29-year-old.
Blues boss Antonio Conte would later put those reports to rest: "I don't know, I don't think so. I prefer to talk to the club to give my opinions. I repeat, I don't want to give my opinion about the transfer market."
But former Liverpool player Nicol believes that if the rumours are true, it means Chelsea are in desperate need of a big-name signing to change their current fortunes.
The London side are currently suffering from a rotten patch of form with summer signing Alvaro Morata's five-game goal drought contributing to Chelsea playing out three successive goalless draws, with just two wins in their last seven games in all competitions.
With Conte said to be concerned with Morata's as well as Eden Hazard's form, the club are reportedly interested in signing West Ham United forward Andy Carroll, who they are currently in talks with as they seek to improve their firepower.
However, with Sanchez's availability, Nicol believes Chelsea are more in need of the former Barcelona man than United, even if he thinks the Arsenal forward would be a better long-term signing for Jose Mourinho's men.
"I think right now Chelsea needs him more," Nicol said, as per Express. "The fact they are trying to hijack this tells you that they are searching.
"It tells you they are looking for a spark or a move or something to get them going. Right now, the form they're in is awful. So Chelsea need him right now, the long-term I think he's better for Manchester United."
Chelsea are currently fourth in the Premier League and lag 15 points behind league leaders City.