The 'club' in question are reported to be Manchester United, with David Moyes having returned to his former employers shortly after heading for Old Trafford in an effort to land one of the Premier League's most consistent performers.
Martinez admits a formal offer was tabled, but says the interested party made it clear that they were reluctant to be drawn into lengthy negotiations.
With Everton having rebuffed the approach, there has been no further movement on the transfer front.
Speculation continues to suggest that Baines could be targeted before the summer window closes, but Martinez insists there is nothing in the reports at present and maintains that the 28-year-old defender will form part of his plans heading forward.
Martinez told the Liverpool Echo: "Before we went to Austria one club officially contacted ourselves with an offer, and it was a final offer.
"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."