Ex-Sunderland and Portsmouth striker arrested in 'gambling investigation' - reports
The Scottish Sun on Sunday reports the investigation involves bets on yellow cards being handed to players among other claims. They report McNulty was arrested last week.
Police officers searched a number of properties in the Edinburgh and Forth Valley areas last Wednesday.
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A Police Scotland statement said: "Police Scotland is investigating reported incidents relating to gambling in sport.
“As part of the ongoing inquiry officers searched a number of properties in the Edinburgh and Forth Valley areas on Wednesday, September 23.
“Two men, aged 21 and 28, have been arrested and released pending further inquiries.”
McNulty spent last season on loan at Sunderland from Reading. The Edinburgh-born forward has also played for Portsmouth, Bradford and Coventry.