The Juventus defender is entering the last six months of his current deal and talks over an extension have broken down.
Arsenal and Chelsea have both been monitoring Lichtsteiner's situation having weighed up moves for the Swiss defender in the past.
And while both clubs could look to hijack United's interest by making a bid for the player next month, Juventus are keen to keep hold of one of their stars for as long as possible.
Manchester United v Newcastle United - Premier League Preview
Manchester United are winning the race for Stephan Lichtsteiner
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That means that Lichtsteiner will be available for nothing in the summer and reports in Spain suggest that United are the frontrunners for the player's signature.
Louis van Gaal is known to be keen to add a right-sided wing back to his squad and has previously looked closely at Fiorentina's Juan Cuadrado.
But Lichtsteiner represents much better value for money, with Cuadrado having signed a new deal with La Viola over the summer, and Van Gaal now appears close to getting his man.