Egan is available as a free agent this summer following his release from the Stadium of Light.
A return to Southend has been mooted, with the 21-year-old having spent four months on loan at Roots Hall in 2013/14.
Brown will be keeping that door open, but concedes that the Republic of Ireland Under-21 international is likely to head elsewhere.
He claims to be aware of interest ‘from a higher level’ and reports suggest that Sky Bet Championship side Blackburn Rovers have joined the hunt for Egan’s services.
Brown said: “We’ve been told by his agent that he will be joining a club from a higher level, but the door is still very much open for him here if he wants to come back.
“I would welcome the chance to sign him and he still hasn’t actually signed for anyone yet.”
Egan, a product of Sunderland’s academy system, helped Southend into the League Two play-offs last season but was unable to see them past Burton Albion.
He has also spent time on loan at Crystal Palace, Sheffield United and Bradford City in the past, but has made just 20 senior appearances in three years as a professional.