Payet is one of the best attacking midfielders in the Premier League and is a key player in the current West Ham squad.
The 29-year-old has scored two goals and created 72 chances in 18 Premier League appearances for the Hammers so far this season.
During the 2015-16 campaign, the France international has scored nine goals and created 116 chances in 30 league matches.
Former West Ham goalkeeper Hislop does not see Payet leaving West Ham for London rivals Arsenal in the January transfer window.
"Payet to Arsenal, I think, depends on Ozil who is asking for an awful lot of money to renew [his contract], has not been that great," Hislop told ESPN.
"This could be a straight swap so that depends on Ozil. I am going to say a miss only because I think Ozil renews at Arsenal, Payet does not join the Gunners.”
West Ham are 13th in the Premier League table at the moment with 22 points from 20 matches and have a good chance of ending the season in the top 10.
As for Arsenal, the Gunners currently find themselves fifth in the league table with 41 points from 20 matches.
The North London outfit are just a point behind Manchester City, who are currently fourth in the standings and occupy the final Champions League spot.