Fon Williams and wideman Zoumana Bakayogo head the list of players whose contracts expire this summer.
Moore accepts Bakayogo may move on to pastures new, claiming Championship clubs are interested in his services, but Fon Williams has indicated a desire to remain on the Wirral and talks with the player's agent could take place on Monday.
"I believe we've got a chance with Fonners," the manager told Rovers' official website. "He wants to stay so we'll wait and see what happens.
"I'd love him to be here next season and he said he'd see me on June 24 when we're back, so we'll wait and see.
"I think Fonners wants it doing sooner rather than later so we'll speak to the agent again and see where we are."
As has been the case since Jake Cassidy's return to parent club Wolves at the turn of the year, Moore will scour the market for a goalscorer during the summer.
"We've got to try to find a striker, someone who is hungry and on the front foot in the box," he added.