Neale is set to meet with St Kilda coach Ross Lyon - his former boss at Fremantle - on Friday night as he weighs a range of options following the public breakdown of his marriage.
The 33-year-old will also reportedly meet with Essendon officials and has had interest from Collingwood, as well as clubs in Western Australia and South Australia.
Fagan wasn't fazed when quizzed about Neale's interactions after Brisbane's 19.9 (123) to 14.17 (101) win over Geelong on Thursday night.
The 65-year-old coach admitted "the ball's in his court" but added the Lions are keen to keep the two-time premiership star and dual Brownlow Medal winner.
"Lachie Neale is a free agent, and he's had a fair few things going on in his life, and he has to be able to deal with that going forward," Fagan said.
"It's not just from a domestic perspective, but financially as well. He has to explore his options.
"Old-fashioned me, I wouldn't like it, but I've come to accept that's the modern game.
"The thing about it is, the only thing I really care about is that he's OK himself and that he plays well for the team - and he's doing that."
Neale shone with 28 disposals and six clearances against Geelong as Brisbane leapfrogged their opponents into fourth spot on the ladder with a fourth straight win.
Fagan rejected suggestions the uncertainty around Neale's future and the public nature of his meetings with rival clubs would unsettle the Lions in their bid for a hat-trick of premierships.
"Probably 10 years ago it wouldn't be too good, it'd be frowned upon, but I think times are changing in that space and that's probably a good thing," Fagan said.
"I mean, if you've got free agency, these things are going to happen, so why get all tied up in knots about it?
"The main thing is, we know that we want him and we love him.
"He's at a crossroads in his life where he has to make a decision, and he's got a lot going on. I'm sure he'll work it out."
Neale's former partner Jules has moved to Perth with the couple's two children since their marriage broke down.
Speaking to Fox Footy after the Lions' win over Geelong, Neale said family considerations will be a key factor in a decision on his playing future.
He insisted nothing has been decided and that remaining at the Lions is still an option.
"I love playing here so I've just got weigh up success, finance and everything that goes along with playing footy," Neale said.
"I'm 33 so probably don't have that long left. I honestly don't know what I'm going to do.
"That's 100 per cent the truth. I'm not sure what I'll decide.
"I'm loving playing for this club and hopefully we can make a run at (the premiership) this year."
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