The club had matched Crewe's evaluation of £30k for the former Shrewsbury hit-man but it seems that the player does not want to drop down a division.
25-year-old Rodgers has already rejected two other teams from League Two, Hereford United and Accrington Stanley have both had bids accepted but the player rejected their advances.
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His agent, Mark Cartwright, admitted: "I don't think anything is going to come of the Swindon interest.
"There are a couple of League One clubs who have shown an interest in Luke.
"Two or three teams have come in for him in the last few days and he's keeping his options open.'' Rodgers, who arrived from Gay Meadow in the summer of 2005, was placed on the transfer list by Alex at his own request, having last started for them in November.
Cartwright added: "This is all about playing football as far as Luke is concerned and he wants to stay at the highest standard he can.''
Rodgers has been lniked in recent weeks with League One and local rivals Port Vale but any move would depend on Leon Constantine leaving Vale Park.