The Electoral Commission is also looking to allegations europhiles broke rules by working together to share campaign materials.
It comes after former Cabinet Minister Priti Patel wrote a letter to the election watchdog last week, in which she claimed Remain “blatantly flout the rules to feed the British people their propaganda”.
The Electoral Commission is already investigating the Leave campaign over similar allegations.
Pro-Remain group Open Britain, formerly Britain Stronger in Europe, has always maintained it complied with spending rules.
The election watchdog has said: “That Britain Stronger in Europe may have failed to report joint spending with the Liberal Democrats, the Labour Party and the Conservatives IN by way of paying for campaign materials and/or co-ordinating campaigns via a daily phone call.
“This matter is under assessment in line with our Enforcement Policy, to determine whether or not the Commission should conduct an investigation.”
In her letter to the commission Mrs Patel cited claims more than £1million was funnelled to anti-Brexit groups by big money donors working together.
Spending rules stated the official referendum campaign teams had to declare any work done with smaller groups, before deducting any funds spent from their side’s spending cap.
Mrs Patel wrote that the “combined (declared) referendum expenditure of Britain Stronger in Europe, Conservatives IN, the Labour Party and Liberal Democrats during the referendum period was £14,496,806”.
She said: “Given the clear prima facie evidence of coordination between these campaigns, it would appear to follow that Britain Stronger in Europe exceeded its spending limit by up to £7,496,806.”
The letter continued: “In addition, Britain Stronger in Europe would have made a false return of referendum expenditure.”
The Guido Fawkes political news site has also been calling on the Electoral Commission to investigate the Remain camp’s spending.
The Liberal Democrats were slapped with an £18,000 fine by the Electoral Commission last year for breaching spending rules.
The pro-Remain party had failed to submit and complete an accurate spending return.
Open Britain were hit with a £1,250 penalty for the same breach.
Open Britain, the Liberal Democrats and the Conservatives have not responded to requests for comment.
A Labour Party spokesperson said: “The Labour Party will co-operate with the Electoral Commission should they decide to open an investigation.”