Southampton are reported to be leading the chase for Scott Arfield, while fellow midfielder Vitor Lima was the subject of a failed £30,000 bid from an unnamed Greek club.
Jackie McNamara is also reported to have received an offer from Partick Thistle.
May said: "Jackie has got an option in his contract that he can go to any team where he can be a coach or manager.
"Jackie can invoke that if he wants, but Jackie will play tomorrow at Rangers."
When asked whether he expects the 35-year-old to be at the club on Tuesday, May said: "Yes, I do."
But May added: "I don't dictate who stays and who goes. It's a financial matter so the people at board level will dictate whether any offer is acceptable or not.
"Hopefully Tuesday comes and we have not lost any players."
Brian McLean is expected to recover from a knock to replace Pele when Falkirk face SPL leaders Rangers.
"It's a big hole in our defence, Pele will be out for a long time," May said.
"There is no finance to bring anyone else in. We are down a few players and we just have to regroup and get on with it."
There is some good news on the horizon for May with Tam Scobbie rejoining the squad to travel to Ibrox following a four-month lay-off, although he is not expected to feature.
The Scotland Under-21 cap has benefited from a period of rest after a recurrence of the pelvic injury that dogged him last season.
Scobbie said: "Last season it was a case of do or die, we had to get points and I was the kind of guy who would always put myself forward whether I was 75% fit or 90% fit.
"I wanted to do it this season but the manager has pulled back the reins and said 'you need to look at the longer future'.
"I'm only 21, he said 'what about five years down the line if this injury keeps cropping up, what will you do then?'
"He tells me he wants me back as quickly as possible but not to the detriment of my body."
Scobbie has returned to training after a period of complete rest was followed by a spell working on his core strength.
A specialist has been "amazed" at the progress made and Scobbie is confident he has overcome the problem.
"It was difficult, I was coming in some days for maybe only 45 minutes and the physio was telling me, 'that's you, go home and rest up'," he said.
"I wasn't really seeing the boys and it got a bit frustrating. They are a great bunch of lads and you want to be in amongst it. I'm still young and full of enthusiasm.
"But, as the manager says, I needed to look at the bigger picture. I had to take time off to recover. In all fairness to the medical staff and manager, it has worked.
"It's proof that taking a step back is sometimes the best way to take a step forward."
Source: Team Talk