Wright-Phillips, 29, looks set to leave City for the second time having failed to establish himself in Roberto Mancini's expensively-assembled first team.
The England winger - who had a three-year spell with Chelsea from 2005 - will not be short of options, but could be tempted to rejoin his former City boss Mark Hughes at Craven Cottage, where he would be set for regular football.
Wright-Phillips agent Wayne Lindsay said on www.skysports.com: "My understanding is that Fulham have made an enquiry for Shaun, as have Newcastle.
"There are two other clubs also showing an interest, one loan and one permanent.
"There is also interest from a French club, but these are all options Shaun will have to consider."