Midfielder McKay told the Tele that he would be open to remaining with Ton until the end of the season if he was still unlikely to get game time with the Ibrox outfit.
The Cappielow club host Queen of the South this weekend, and the match is the final fixture covered by 19-year-old McKay’s initial one-month deal.
Although Shiels believes Gers gaffer Ally McCoist will be keen to keep the midfielder in Glasgow, he will make enquiries to find out whether there might be an opportunity to renew the loan.
The Ton boss told the Tele: “I would definitely be on for extending Barrie’s loan if Rangers were happy enough to do that.
“I’m sure they’ll be wanting him back, though.
“They’re understrength at the minute with the boy [Nicky] Clark out injured.
“But I’d definitely be interested in keeping Barrie for longer.
“I’ll make a phone call to see what the situation is.”
Meanwhile, former Celtic and Hibs striker Derek Riordan did not train with Morton as expected yesterday.
The 31-year-old free agent was pencilled in to participate at Parklea but is thought to be close to securing a move to Belgian second tier side Royal Antwerp.