The 31-year-old was in the form of his career for the Robins while on loan in the first half of the campaign, scoring 23 goals in 24 appearances, and admitted disappointment at being recalled by his parent club in the New Year.
Swindon have now moved to make a permanent move for the Irishman, however, with the Bantams expected to accept rather than lose him on a free in the summer.
Both Doyle and teammate James Vaughan, who has been linked with a loan exit from the club, were left out of the Bradford side that were held to a 1-1 draw with Cheltenham Town last night.
"We have received offers for both of them," Bradford's director of comms Ryan Sparks told the Yorkshire Post. "And those offers are currently being considered by Eoin, James and, of course, the manager (Gary Bowyer).
"The James Vaughan offer is in the form of a loan agreement until the end of the season. Eoin's would be more permanent. Obviously, he can only play for two clubs in one season and that is as much as we can say on that at the moment."
Sparks continued: "Prior to Eoin returning to Bradford City he made it quite clear, publicly, that he would prefer to be at Swindon Town. He has expressed a similar desire on that note and we have in turn received the offer from Swindon Town."
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