Clubs from the Championship have made their interest known and May feels that will be his destination when his Falkirk contract expires at the end of the campaign.
When asked whether Hibs had been in touch, May said: "They have been but Darren will go down to England.
"There have been a couple of clubs down there (who have shown interest) and I'm sure at the end of the season he will go and play his football down in England.
"I had a conversation with him last week, Darren won't be signing a pre-contract with anybody.
"He will leave his options open until the end of the season and I'm sure he will get the right club."
May also allayed supporters' fears that Barr may be sold in January to avoid him leaving for free.
"I think Falkirk have had great service out of Darren," said May, who was instrumental in Barr's first-team breakthrough in his previous role as youth academy boss.
"The money they have paid him over the years, and what he has given the football club, I'm sure Falkirk have had their money out of Darren Barr.
"He will stay until the end of the season and I'm sure we'll get our worth in what Darren has brought to the football club and what he'll bring in the second part of the season."
There will be some departures in January though, with loan players such as Kjartan Finnbogason and Alex MacDonald still waiting to hear whether they will be offered extended deals.
"Some will go, some will stay," May said. "I will need to tell them that first and I'm sure I will tell them that in the next 10 days."
May, who will have new signing Toufik Zerara in his squad for Saturday's SPL clash at St Mirren, added: "I think 80% of the guys we have brought in have done the job successfully. The other 20% have not been good enough.
"You can't get them all right but if you get 80-20, that's decent business.
"If we bring players in I'll be looking to boys who have not featured very much to go out on loan or go elsewhere.
"We'll definitely adjust the numbers because it's no use having so many players when you can only play 11."
Falkirk visit Paisley four points adrift after their 3-1 defeat by Rangers was followed by victories for their closest rivals, but May is unconcerned by the league table.
"I've always maintained that we'll be where we are at the end of the season because of what we've done, not because of what other teams have done," he said.
"I'm not really interested that Hamilton beat Hearts or that Kilmarnock beat St Johnstone.
"If we don't win games we'll get relegated. We have to concentrate on what we do and not what other teams do."
Meanwhile, May has apologised to Willie Collum after criticising the referee for missing a handball by DaMarcus Beasley before awarding Rangers the penalty that led to their third goal.
"I criticised the referee in terms of I didn't think it was a penalty," May said.
"I still maintain that but, what I didn't appreciate at the time was that there was a guy standing in front of the referee and he couldn't see a thing.
"I would like to apologise for that."