Foxes boss Craig Shakespeare tried and failed to sign the 26-year-old in the summer after he played a key role in helping Palace stave off relegation to the Championship under Sam Allardyce's guidance in the second half of last season.
A £27million bid was said to have been rebuffed by the Eagles, but reports are now claiming that a fresh offer will be forthcoming in the New Year.
Palace had no intentions of losing Townsend but it is being suggested that, as key striker Christian Benteke is struggling with a knee injury and facing another month on the sidelines, current boss Roy Hodgson will sell Townsend to raise funds to add another quality forward to his options for the second half of the season.
At the moment, Townsend's fit-again fellow winger Wilfried Zaha looks like returning from injury in a striker role when the Premier League resumes against reigning champions Chelsea at Selhurst Park this weekend due to the lack of options in that position.
There is also the possibility that Townsend might push for a move in January given that Palace are currently rooted to the foot of the table having become the first team to have lost their opening seven matches without scoring a goal.