However, the Championship side see the 30-year-old keeper as one of their prize assets and are reluctant to let him go at any point.
The goalkeeper is reportedly regarded as irreplaceable by the club, with Russell Slade’s side on track to push for a promotion place in the second half of the campaign.
That has led to them setting a big price tag upon his head, with Wales Online claiming they will ask for £10 million for their man.
Everton’s interest comes as they reportedly look for a replacement for current number one Tim Howard.
The American has been heavily criticised this season, with his side having conceded 29 goals already this season and managing just five clean sheets in total.
A move for Marshall seems unlikely though, with it more likely they will hand a chance to number two Joel Roble, who has impressed in the cup competitions.