Arsenal beat Aston Villa 4-0 at Wembley on Saturday to retain the??oldest knockout trophy in football, Theo Walcott, Alexis Sanchez, Per Mertesacker and Olivier Giroud finding the net to earn the Gunners a record-breaking 12th FA Cup triumph.
A third-placed finish in the Premier League has also guaranteed direct entry into the Champions League but Wenger, who became the first manager in the post-war period to win six FA Cups, has swiftly turned his focus to the next campaign.
“I think of course we can push on,” the Frenchman said.
“Why not? We have won the league in the past when we had the potential to do??it and that is what we want to do again.”
Wenger may have had his critics over the second half of his 19-year reign in north London but admitted his “great hunger” means he is in no desire to end his love affair with a club he joined in 1996.
“I have two more years of contract and I will sit down with my directors and see how much they believe and trust,” he added.
“My hunger is great but I want to do well.”