"We are following up to understand the circumstances, but no, I would not term it a formal investigation," NHL deputy commissioner Bill Daly said.
There's a Twitter photo of Turco, sitting at the end of the Blackhawks' bench, apparently accepting a $5 bill from a fan.
Blackhawks coach Joel Quenneville smiled Wednesday while addressing the incident.
"It's something that happened, we're handling it internally," he said.
Someone describing himself as a Canadiens season-ticket holder called a Montreal radio station and said the bet was made after Mike Cammalleri put Montreal up 1-0 in the second period.
"I bet him after the Canadiens scored that Chicago wouldn't score again," the caller said.
After the Blackhawks' Patrick Kane tied the game minutes later, money allegedly was exchanged.
"When they scored ... I gave him five bucks," the caller said. "I slipped it through the glass. He took it with no questions whatsoever. I wrote on the $5 bill with a Sharpie, 'Habs rule.' "
"I went triple or nothing after the second period, nobody scored. Into the overtime, I went, 'Marty, I'll give you 5-to-1 the Canadiens win the game.' He took the bet. When the Canadiens scored in overtime, he handed me back a wad of $5 bills. And inside ... was the $5 bill that I gave him that he crossed out 'Habs rule,' and wrote 'Turco rules.' "
In a text to ESPNChicago.com, Turco said: "I gave back his five, and wrote something back, yeah."
The fan told the Chicago Tribune that what he said was that it was a wadded up $5 bill.
The defending champion Blackhawks are fighting for their playoff lives. After beating the St. Louis Blues in overtime on Wednesday, Chicago holds the eighth and final playoff spot in the Western Conference with two games to play -- both against Detroit.
Turco signed a one-year, $1.3 million contract with the Blackhawks, who walked away from Antti Niemi last summer when an arbitrator awarded him a $2.75 million judgment.
It has been a disappointing season for Turco, who is 11-11-3 with a 3.02 goals-against average.
ESPNChicago.com's Jesse Rogers contributed to this report.