The Owls stopper, currently out injured with a knee injury will be offered a new and improved contract in the next few months because Paul Sturrock believes his position is vital to the team.
Lucas originally signed on loan from Preston but his spell was cut short with a knee injury, but Chris Turner made sure he was one of the first players he brought into the club last summer.
McGovern meanwhile has been out all season and reports have indicated that the Scottish winger is wanting a new deal otherwise he will assess his options.
The former Celtic player, like Lucas is out of contract in the summer but Sturrock is making sure McGovern gets back to fitness first before any talk of a new contract materialises.
Meanwhile only a few hundred tickets are available for Wednesday's trip to Watford at the weekend and the game at United has sold out for away fans.