Slane has not yet signed a pre-contract deal but Brown is resigned to losing the promising winger, and has already lined up a replacement in former Celtic youngster Michael McGlinchey.
"It's inevitable that Paul Slane is going because Celtic have made an offer to take him," Brown said.
"The chairman and the board are discussing that offer, but it's apparent that Paul will be leaving.
"They have to make a compensation offer because we gave him a very good three-year deal, which he declined.
"He was giving us good provision on the bench or even starting later in the season but we won't consider that now because we have got to look to the future.
"When Michael McGlinchey comes in, he will more than cover that.
"I don't think it's productive for Motherwell to play Paul in the team.
"He might help us in the very short term but we have got enough provision without having to use Paul. We want to improve our own players and not improve players for other teams."
Celtic have sourced Fir Park numerous times over the decades for players such as Dixie Deans, Joe McBride, Brian McClair, Andy Walker, Phil O'Donnell and current top scorer Scott McDonald.
But Brown, who continues his interim management campaign at Falkirk on Wednesday night, admits it is a worrying trend to see players leave before they have established themselves in the first team.
Slane featured heavily in Motherwell's Europa League campaign but he is yet to start a Scottish Premier League game after undergoing two calf operations this season.
"He's 18, on the fringes of the team," added Brown, who hopes to add a defender to McGlinchey's impending arrival.
"The time to go, in my opinion, is when you are established - when you have been Brian McClair, Scott McDonald or James McFadden or (David) Clarkson and (Paul) Quinn, who went recently to Cardiff.
"But it's hard to advise a player and his agent to wait when they see an opportunity to go, so that's their decision.
"We can't compete. He's a Celtic fan and, when he sees the hoops and they want him, it's hard.
"Money couldn't compete, not that money is a priority for all players, but the lure of getting on that Celtic jersey for Paul is too great for us to match."
Brown has a perfect SPL record with Motherwell after victories over Kilmarnock and St Mirren gave the Steelmen consecutive SPL wins for the first time this season.
But he anticipates his hardest test yet at bottom club Falkirk, who lost 4-1 at home to Dundee United on Sunday.
"The two wins could bring complacency," Brown said. "They have played fairly well in patches in both matches we have won, but this is a more difficult assignment in my opinion because Falkirk are hurting after their defeat.
"They are a better team than that result showed, we saw that against Celtic.
"When a team is fighting for its life, it's a very difficult away game and we have got to be up for that."