May is currently on personal leave and hasn't been at Demons training in recent weeks.
The 34-year-old May and Richmond midfielder Dion Prestia are fighting criminal charges after a late-2024 brawl in Sorrento on Victoria's Mornington Peninsula.
May and Prestia last month asked for the charges to be withdrawn, saying they were not there.
In a separate matter, police were called to May's house last month, for undisclosed reasons.
"He's on personal leave. That's really as much as I can give you," Gawn told AAP.
"I've reached out to him. We're in dialogue.
"I don't reach out about anything I shouldn't, and don't want to go into his face. I just make sure that he's healthy and well and he's away from the club at the moment."
May, who is contracted until season's end, was told to explore his options by new coach Steven King over the off-season after a disappointing 2025 campaign.
But with no suitors, the fullback returned to Melbourne.
The key defender was an All-Australian in Melbourne's 2021 premiership season and again in 2022, and Gawn had faith May could yet play a role again.
When asked if he was hopeful May could come back and play again, Gawn said: "Always hopeful.
"He's a premiership player and a very, very decent fullback.
"So, yeah, hopefully that all gets worked out at some point."
When asked if he would look to regularly check in on May, Gawn said: "I do that with all my 45 players - and past players, to be fair - so you can add another 50-to-60 to that.
"And then there might be some that have an asterisk to it that I need to make sure I'm doing more than once a month.
"And right now, because Mayzy is taking time away from the club and I'm not seeing him face-to-face, he is someone I'm checking up on, yes."
Melbourne kick off their 2026 season at the MCG against St Kilda on Sunday 15 March.
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