Antonio Conte is looking to complete the double in his first season at Chelsea, mirroring Carlo Ancelotti's debut campaign at Stamford Bridge in 2009.
The Blues won the Premier League with two games remaining, finishing with a record 30 wins from their 38 matches, seven points clear of Tottenham in second.
And McLeish has been impressed with the west London outfit, especially in big games this term.
"I think Chelsea have been so good this season that I can't see them being stopped," he said on talkSPORT.
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Antonio Conte and Arsene Wenger go head-to-head in the FA Cup final tomorrow at Wembley
But for me, I'm going to go for Chelsea in the FA Cup final
Alex McLeish on Arsenal v Chelsea
"They have been a bit of a juggernaut when it's come to the big games."
Arsene Wenger's Arsenal ended their season strongly in the league, winning seven of their last eight matches.
Wenger is out of contract at the club in the summer and there has been no announcement as to whether he will extend his stay at the Emirates.
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Alex McLeish thinks Antonio Conte's Chelsea will beat Arsenal in the FA Cup final
McLeish believes it's typical for the Gunners to up their form for Wenger towards the end of the season but still can't see them trumping Chelsea tomorrow.
"Arsenal have finished the season strongly, nothing surprises you with Arsenal at the end of the season," the former Birmingham manager added.
"When you think that Arsene's going to leave for the last five to six seasons and then he comes out with about five or six good results.
"But for me, I'm going to go for Chelsea."