The Gunners' title hopes have been damaged following a humiliating 6-0 defeat at the hands of Chelsea on Saturday.
Following the mauling at Stamford Bridge, it has been confirmed that the Frenchman will not hold his scheduled 9am press conference on Monday previewing Tuesday's match against Swansea City.
While there may be questions regarding Wenger's future, Lawrenson believes that he will stand by the North London outfit as they are currently two wins away from clinching the FA Cup.
Lawrenson wrote in The Mirror: "Arsene Wenger won't walk away from Arsenal. And even if he were thinking about it, he certainly wouldn't go before a possible FA Cup final. Having taken the club to the brink of their first trophy since 2005, I can't see him just leaving now.
"Having said that, I can see why the grapevine was buzzing after the Gunners boss cancelled his Monday press conference ahead of the game against Swansea."
Widespread reports have suggested that a Wenger could sign a new contract at the Emirates in the summer.