But he has instead agreed a three-year contract with St Johnstone.
"Liam had an offer to stay with Falkirk and interest from other clubs which would have been more lucrative," said McInnes, who will lead his First Division side out at Hampden against Rangers on Sunday.
"But he feels his footballing interest is best served by staying at McDiarmid Park and that speaks volumes for him.
"Fans will be aware how important Martin and Peaso have been to us in recent times and to have them pen two-year deals is a great boost as well."
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