The Daily Record says the SPL champions have been studying the 31-year-old Pole's form and are favourites to land him ahead of Hearts and a couple of English clubs. However, if Szamotulski is snapped up it would not mean Artur Boruc heading for the exit.
Celtic are determined to use their option of holding on to Boruc for an extra year which would keep him in Glasgow until May, 2010.
But they do see the keeper nicknamed the Monk as an extremely capable addition to their squad and the fact United can't claim a transfer fee also holds appeal.
Szamotulski, who has been with a number of clubs and arrived at Tannadice from Sturm Graz, would be able to squeeze the salary he believes he deserves from Celtic.
Hearts have money to spend from the £9million transfer of Craig Gordon and could pay much more than United, who tried hard to extend his contract beyond December 31, but the chance of joining Boruc at Celtic Park could be too much to resist.
Szamotulski will look for £8000 to £10,000 a week and that wouldn't make anyone at Parkhead flinch.