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Gillingham rejected a deadline-day offer for John Egan and hope to secure his services long-term.
The Irishman was the subject of a bid from Championship side Brentford on Monday but they were knocked back by Gills chairman Paul Scally.
Mr Scally had also rejected a £2m offer from Bristol City for leading scorer Bradley Dack.
Egan, 23, is coming to the end of a two-year contract at the Gills, having been signed after his release by Sunderland, and the club have an improved offer on the table.
Gills boss Justin Edinburgh believes the offer is a "very good one" but may have to wait until the summer before the situation is resolved. Egan could walk away for a nominal amount when his contract expires as he is under the age of 24.
Confirming the Brentford bid, Edinburgh said: “The offer didn’t meet the chairman’s valuation, or mine. We spoke to John, made him aware of it and we didn’t hear any more.
Edinburgh has a number of players out of contract in the summer but Egan is a valued commodity and the Gills will want to tie him up on a contract.
The Gills boss said: “John wants to concentrate on the football side and I understand and respect that. The ball is in his and the representative’s court. It is ongoing.”
Egan has made 84 appearances for the Gills and has worn the captain’s armband during Doug Loft’s absence.