Assaidi joined Liverpool in August 2012 from Dutch side Heerenveen but made just 12 appearances for the Merseyside club last season.
The Morocco international was loaned to Stoke before the start of the current campaign and has impressed for Mark Hughes' side, scoring four goals in 22 games, including a late winner against Chelsea in December.
The 25-year-old is unsure where his future lies, but has urged Rodgers to give him another opportunity to impress at Anfield.
"I'm unsure what Stoke or Liverpool wants," he told Stoke's official website. "I am really happy to play for Stoke and I am happy they gave me a chance to play regularly.
"I get on well with my team-mates and I'm very happy playing for the manager here. The club is good for me and my time here has been a good one.
"I still have a contract with Liverpool and I hope the boss gives me a chance.
"If not, I do not want to sit on the bench because I want to play games so you never know what can happen in the future."
Assaidi has not featured for Stoke since February because of a knee injury, however, he is hopeful he will be able to return to action in the near future.
"Things are certainly getting better, but my knee is still not fully healed," he added.
"I could forget about the pain and play, but that would be a massive long term risk, so I believe it's best to be patient and wait for it to get better before playing.
"I am recovering well so I hope it isn't too long until I can be picked to play again."
