The 27-year-old has been on loan with the Championship sides for two spells this season, having initially been recalled to Craven Cottage in December before heading out again in January.
|13/5||Fulham are 13/5 with BetVictor to beat Liverpool on Sunday
"I will be going back to Fulham some time this week," Stockdale told talkSPORT.
"Unfortunately my chances at Fulham have been a bit limited. Although I love the club, maybe it's time to move if pastures new come."
Stockdale has been playing second-fiddle to Mark Schwarzer at Craven Cottage, with the Australian recently admitting he could leave the club in the summer, though manager Martin Jol is keen for him to sign a new deal.
Meanwhile, Hull manager Steve Bruce said in April that he would be interested in signing Stockdale permanently if they were to be promoted, stating: "I don't think it is set in stone, but it is something that has been discussed.
"There is certainly the possibility of a deal to be done if we were to get to the Premier League. That is where Stockdale wants to play and that is where we all want to play."