The 27-year-old former Everton man has been a key performer for Steve Tilson's side this season but has delayed talks on a new contract with the club.
His current deal expires at the end of the season but Martin hasn't given up hope that Clarke will opt to stay at Roots Hall.
"I understand that players like to keep their options open and we will be talking to Peter at the end of the season," he told the club's official website.
"He hasn't said he wants to leave and he has always been committed to Southend United during his three years here which is admirable and I'm sure that will continue.
"No new talks have taken place recently because Peter told us he wanted to concentrate on his football which is fine but he's a player we would very much like to stay."