The Gunners have not won the Premier League title since going through an entire season unbeaten in 2003-04 and have been unable to launch a genuine title challenge since moving to the Emirates Stadium in 2006.
Thomas - who memorably scored a last-gasp goal against Liverpool to win Arsenal the title in 1989 - praised Wenger's contribution to the club during his 21-year reign, but suggested that it could be time for the Frenchman to step down from his role.
"[The 4-1 win over Palace on Saturday] was fantastic, but that's Arsenal. They are always going to win games, no matter who is playing. However, for me, the most important thing is to win the league," he told Sky Sports News.
"They've not progressed. They've won the FA Cup and it's still a big thing but the league should be their bread and butter. Arsene Wenger has been fantastic for the club and I love what he's done for the club, but anywhere else he wouldn't be there because he's not won a major trophy for a long time.
"Anywhere else, especially abroad, he wouldn't be there long enough. It's down to the board and they should be doing something about it. The golden thing was that we left Highbury to move to a bigger stadium and compete with the big boys and win big trophies. Has it happened yet? It hasn't."
Arsenal currently sit sixth in the Premier League table, five points adrift of the Champions League places.