Vicente Guaita has been identified as a top January target by the veteran manager, and the Eagles have already discussed an initial £3.5 transfer with Getafe for the goalkeeper, reports the Guardian's Ed Aarons.
Guaita's contract in the industrial Spanish city expires at the end of the season, but Hodgson is keen to complete various transfers this month as he attempts to stave off the threat of relegation. If Crystal Palace succeeds in surviving the drop, Getafe would apparently be due an additional, undisclosed payment.
Watford is understood to be another party interested in Guaita, but Crystal Palace is leading the pack chasing his signature.
The 31-year-old has helped Getafe to a surprise 11th-placed standing in La Liga this term, conceding just 16 goals in the 17 games in which he's appeared. He was tipped as a future international star when he emerged from the Valencia academy, but had to rebuild his career after a downturn in form which eventually led to his 2014 transfer to Getafe.