The 28-year-old defender has been the subject of intense transfer speculation this summer, with suggestions he could leave Goodison Park before the start of the 2013/14 campaign.
Former manager David Moyes has been credited with an interest in bringing Baines to Old Trafford, after he replaced Sir Alex Ferguson as Manchester United manager in May.
Martinez confirmed that a formal offer for the England international was tabled from an unnamed club - thought to be £12million from Manchester United - earlier in the transfer window, but after knocking back that initial bid, nothing has been heard since.
"Before we went to Austria one club officially contacted ourselves with an offer, and it was a final offer," the Toffees boss told the Liverpool Echo.
"They put something over and the valuation wasn't anywhere near the quality of Leighton Baines.
"That was the end of it but since then there's been all the speculation, which has been part of what the transfer window is.
"There's never been another club or anyone else putting in an offer for Leighton. Since then we've moved on and we're continuing to focus on the start of the season."
With Patrice Evra and Alex Buttner already part of the Manchester United first-team, Moyes is not desperate for another left-back addition, and this could prove to be the reason why they have not followed up their initial enquiry with an improved bid.