The England Under-21s international, who impressed for Bristol City with 23 goals in the Championship last term, is said to be close to sealing a season-long switch to the Swans.
Abraham had previously been strongly linked with a move to newly-promoted Newcastle, though reports emerged last week suggesting that he had been urged by Chelsea to instead seek a temporary switch elsewhere to avoid being tempted by the North-East nightlife.
Writing in his Newcastle Chronicle column, Quinn hit out at Abraham for choosing the 'smaller club' in Swansea.
"I have to say I am extremely disappointed in Tammy Abraham," he said. "If he really is set to choose Swansea City over Newcastle United, I would seriously question his decision. It shouldn't take me to tell him that Newcastle is a far bigger football club than Swansea. I admit I didn't release just how huge a club Newcastle was until I signed, but I always knew it was a big club.
"It's obvious to anyone outside that Newcastle is one of the top few clubs in the country. And you just have to look at the situation at both clubs at the moment as well. At St James' Park there is a club on the up with a world-class manager who can really go places if Rafa Benitez is backed.
"At the Liberty Stadium, you have a club who only just survived last season and are likely to be battling relegation again next term. True Abraham is only going to be loaned out for a single season, but does he want to experience playing football in front of a pressurised environment?
"St James' Park, in front of 52,000 passionate Geordies, is the place for that. I don't know Abraham personally and I don't know his exact reasons for choosing Swansea over Newcastle but, quite frankly, any excuse would be weak in my eyes. If he doesn't realise that, then perhaps it's best he has chosen to go elsewhere after all."
Abraham is currently representing England Under-21s at the European Championship finals in Poland, where he has so far failed to net in his three appearances.