The Eagles chief is desperate to help keep the Londoners in the Premier League as the side have endured a nightmare start to the season with an historic seven successive defeats in which they have also failed to score a goal.
The start cost Frank de Boer his job after just four of those games, while Hodgson has oversaw three defeats since stepping into the hotseat.
Injury issues to key players like Wilfried Zaha and Christian Benteke have not helped the situation at Palace and, while Hodgson must muddle through until January, he will no doubt recognise that he must bolster his ranks in the New Year window in order to help stave off relegation to the Championship.
Reports claim the former England boss is already casting his net to sound out players who have plenty of top-flight experience who he feels could come into the club and hit the ground running and make an impact.
Wilshere, who he knows from his time in charge of the Three Lions, is one of those players who could do a solid job for Palace.
The 25-year-old has only just returned to action after fracturing his leg while on loan with Bournemouth last season, and has set his heart on fighting his way back into the Arsenal side after turning down several moves on deadline day.
However, if he has been unable to play his way back into the thoughts of Arsenal boss Arsene Wenger by January, there is a good chance he could seek another loan move, and the Eagles will be at the front of the queue.