Andrew Hamilton, secretary for the APMI, said: "What he [Swinford] told us was very interesting."
Hamilton said Swinford made an offer to refund any deposits already paid by exhibitors for Northprint if they transferred to exhibiting at Print UK.
"In fairness it was conditional upon Northprint not taking place, to make sure exhibitors did not lose out by going to Print UK," said Hamilton.
Northprint 2003 takes place at Harrogate Exhibition Centre from 13-15 May, while Print UK is at the NEC in Birmingham from 1-3 April.
Northprint exhibition director Andrew Furness said it was the first he had heard of any offer. "We have had no firms withdraw from the show, quite the reverse," said Furness.
"We stand by what we have done with Northprint, but at the same time we are aware we cannot sit still."
Swinford said: "What we have said is that if companies wish to go to Print UK and cancel their booking at Northprint, we will look upon them sympathetically."
One exhibitor, which had already paid a deposit on a stand at Northprint, said it had been offered the deposit return if it switched shows.
"We feel Northprint will be devalued if some of the machinery exhibitors take up the offer and pull out," said a source at the firm.
"At the end of the day we hope exhibitors will go with the show that offers them best value, and suits their market," added Furness.
Story by Andy Scott