Heading the list at the moment are Rangers, who have once again been linked with a £1million move for the SPFA's young player of the year.
But Brown insists Kilmarnock have yet to be given reason to believe their prize asset will be going anywhere this summer.
Brown said: "Until a bid comes in, it's hard to say that we're resigned to losing him.
"We just hope there is someone we can bring in if Naisy does go, but he's down on my list for pre-season training in Italy at the moment.
"When you've got someone of Steven's talent, will and endeavour, big clubs are going to be watching him. There have been scouts at every Kilmarnock game.
"He's the young player of the year for the SPFA and was the sports writers' choice last year so you can't stop people looking at him."
Another player Kilmarnock are keen to keep is Eric Skora, even though he has not kicked a ball in anger since his January move to Rugby Park.
Skora was a big hit during his first spell at Kilmarnock - a loan deal from Preston in 2004 - but a knee injury has denied him any appearances this season.
Even so, the midfielder is set to be handed a contract extension which will keep him at the club until the end of the year, while Aime Koudou has been told to use the last four games of the season to win himself a new deal.
Brown said: "We're looking towards next season for Eric to be honest.
"We're looking to get him fixed up for a short period, probably until the next window, because he is a player who did well here.
"Obviously with his knee injury, we have to assess that he is up to it, but I'm sure he is. We intend to try to keep him here.
"With Aime Koudou, we're hoping to have a look at him over the next three or four games."
Meanwhile, Kilmarnock are close to completing the signing of Craig Bryson from Clyde, with the formalities expected to be sorted out following the Bully Wee's final game of the season on Saturday.
"He's one that we're looking at," said Brown. "But it's not fixed up yet.
"He's still a Clyde player at the moment and it's hard to talk about until after Clyde's last game but we hope we can sort that one out."