The 29-year-old, who joined Albion on a free transfer in the summer of 2011, has not made a first-team appearance since the FA Cup third-round defeat at Leicester on January 5, when he came on as a substitute after 62 minutes.
His last start came in the league loss at Barnet on December 21.
Chris Palmer had his contract at the Pirelli Stadium terminated by mutual consent last Friday and fellow midfielder Taylor may end up in the same boat.
"Cleve has been a model professional while he's not been in the team with the way he's conducted himself," Rowett said. "At this stage of his career, he needs to be involved though.
"I've spoken to him. Like Chris, he's not been in out plans. If we could help him find somewhere else, or maybe come to some sort of settlement, then we'll look at doing that."