The retrospective of Vettriano's work at Kelvingrove Art Gallery and Museum in Glasgow has so far attracted more than 83,000 visitors.
That figure, officially recorded last week, is now, unofficially, likely to be around 90,000, museum sources say.
Kelvingrove's record was set by the Glasgow Boys show in 2010, which attracted more than 120,000 visitors as well as wide critical acclaim.
The Vettriano retrospective this weekend was busy with visitors seeing the one-off show by the self-taught Scottish painter.
Demand for the show led to the museum, for the first time since 2006, opening late for one night in November.
The show runs until February 23 but organisers are expecting a late push for tickets as the show is very unlikely to be staged again after it closes.
Vettriano, whose popular images have sold millions of copies as prints worldwide, has spoken of his gratitude to Glasgow for providing the stage for the major retrospective.
It has featured more than 100 of the artist's paintings, including some of his best known images, such as The Singing Butler, Dance Me To The End of Love and The Weight.
A spokesman for Glasgow Life said: "The response to the Jack Vettriano retrospective has been outstanding, with tens of thousands of visitors flocking to Kelvingrove.
"Whether it breaks the attendance record will be a close-run thing.
"But we expect a surge in numbers when visitors realise they have just a few more weeks before the exhibition closes."
Vettriano has not achieved wide critical acclaim for his work, but he said - at the launch of the show - that he expected it to be successful.
He said: "I doubt many critics have ever been to an exhibition of mine, to tell you the truth but I think they will go to this, because it is national, and I think I will get a lot of flak.
"But what I hope happens is that we break attendance records, and I don't see why we can't."