Chris Tarrant presents the television quiz
Colin Hallett, from Essex, was jailed in 1990 for arson.
But it is now claimed that he failed to tell the programme-makers, Celador, about a separate offence four years ago.
In 1997 the 46-year-old window cleaner from Shoeburyness was fined for driving away from a petrol station without paying.
But the show's creators, Celador, say no-one can appear as a contestant if they have a recent criminal record.
Checks continue
The company has now confirmed that it is investigating Mr Hallett's circumstances.
A spokeswoman said: "We can confirm that we are verifying Colin Hallett's eligibility to appear on the programme.
"He has not yet received his cheque.
"We are speaking to Mr Hallett and he is providing us with the relevant documentation."
She added that there was "no problem" with the arson conviction because it was so long ago.
According to The Sun newspaper, Mr Hallett failed to declare that he was fined for making off with £5 worth of petrol from a filling station.
Two-year sentence
He told the newspaper: "I'll be gutted if for the sake of £5 I won't get a penny of the £125,000 I won."
Mr Hallett had received a two-year jail term after setting fire to a shop.
It is not the first time that Celador has acted to stop a winner's cheque.
The company is currently embroiled in legal action following its decision to withhold £1m from Major Charles Ingram.
Major Ingram, from Wiltshire, is being investigated by Scotland Yard over claims that he was helped by someone in the audience.
He has denied the charge.