Chesterfield are keen to sign the centre-half while League Two rivals Fleetwood, who have had a bid rejected, and York are also interested.
Rotherham-born Cresswell has a year remaining on his contract at Roots Hall but is eager to return closer to home and Chesterfield is his preferred destination.
The 25-year-old reported back for pre-season training on Monday along with the rest of the Shrimpers squad when Brown took the opportunity to try to convince one of his prized assets to remain with the Essex club.
An optimistic Brown told the Southend Echo: "Ryan sat down with myself, Dave Penney and Graham Coughlan to have a chat about things and he seemed interested in what we had to say to him.
"He could see that we had a very good backroom team now in place and the work which had also been done at the training ground to make it look much better.
"He wanted to know what players we were looking to bring in so we spoke about our transfer targets and who we wanted to bring to the football club.
"He seemed very receptive and now one of my main aims is to make Ryan want to stay with us because he's a good player and would be a big part of the team next season."
It has been suggested that Chesterfield might try to use Sam Togwell as a make-weight in a deal for Cresswell but Brown insists he is not interested in the Spireites midfielder.
He added: "I think that's maybe something Chesterfield have suggested but it's not something I would be interested in doing."