The operator runs services between Newcastle and York, Leeds and Manchester Airport.
The RMT has criticised First Group and claimed they are sitting on big profits.
The RMT's acting regional organiser for the North East, Craig Johnston, said he thought members would vote to strike.
He said: "First Group are making hefty profits and we are not going to be told that we can pay our way through a recession while they profiteer.
"We're not going to be walked over, First Group need to return to the table and open their wallets. It's one of the worst offers that we have had and that's why members will think it isn't good enough.
"Our members work unsociable hours and provide a good service to the public."
The union's general secretary Bob Crow said: "First Group is generating massive profits and dividends for its shareholders off the hard work of its staff and an offer of just over 2%, while real costs of living on things like gas, electricity and housing are roaring ahead, is simply unacceptable."
A spokesman for First Group said the ballot was unnecessary at this time.
He said: "We remain hopeful that this dispute can be resolved through further discussion and urge the RMT to accept the company's invitation to continue talking."
First Group said around one in ten of its drivers were members of the RMT.
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