The Gunners made a number of attempts to bring the Uruguay international to the Emirates Stadium last summer, but they will not resurrect their interest at the end of the season.
But Wenger has ruled out a fresh attempt at luring the in-form striker to north London.
"It didn't come off and that's it. He was never our player," he told reporters.
Suarez has since been welcomed back into the Liverpool fold, and has helped the Reds push for a place in the top four of the Premier League with 23 goals in 19 appearances.
Arsenal faces Liverpool at Anfield on Saturday and can go 11 points clear of the Reds with victory, but Wenger believes Brendan Rodgers' side, unbeaten in seven matches, is in better shape than when it was beaten 2-0 at the Emirates Stadium in November.
"Liverpool are in a better position than when we last played them," he added. "They have momentum. Saturday is a good moment for us to win a big game because we have a big month ahead. We had some good wins at Anfield. I have a lot of respect for the fans there, they know their football
"I think they are strong offensively with [Daniel] Sturridge, [Luis] Suarez, [Philippe] Coutinho, [Raheem] Sterling and [Steven] Gerrard. We need to dominate the game in order to keep Suarez and Sturridge quiet. We must control possession."
Wenger also confirmed that Jack Wilshere is in line to play some part against Liverpool at Anfield on Saturday, while Mikel Arteta is likely to feature.
Wilshere has not played since the 4-0 FA Cup victory over Coventry City on Jan. 24, while Arteta looked to have picked up an injury during the closing stages of the 2-0 win against Crystal Palace on Sunday.