Hodgson's current Selhurst Park deal expires at the end of this season and the Eagles hierarchy are planning for next season fully expecting the former England manager to remain at the helm, says the Daily Mail.
The two parties have been in talks about a new one-year deal to take him up to 2021 since the early part of this season.
An extension for Hodgson, 72 and the Premier League's oldest ever manager, seemed a formality following Palace's impressive start to the season which saw them sitting as high as fifth at the start of December.
However, they have been hit by a crippling injury crisis which has contributed to a run of one win in their last 11 games, though including six draws.
The Eagles hierarchy believe they can resolve any concerns Hodgson's may have about the club's transfer plans after two underwhelming windows and give him the reassurances he requires to remain in charge.