Barr's contract expires this summer and he has already been in negotiations with rival clubs.
Aberdeen are trying to land him this month - without paying a fee - rather than scrapping it out for his signature on a pre-contract.
May said: "Darren has got a number of options, four in Scotland and I believe a couple down in England as well.
"But Darren is very focused. He doesn't get involved in the financial part, but he obviously has a figure in his head that he wants. He also wants to go to the right club.
"I've been speaking to Darren and he is more than happy to stay here for the remainder of the season.
"Darren has not once said he wants to leave Falkirk this season and is more than determined to leave us in this division.
"He is more than happy to stay through until the end of the season."