Ritchie Jones is thought to have held discussions with Hearts in regards to a summer switch.
The youngster was released by Manchester United at the end of last season and has been keeping his options open during his search for a new club.
He had been widely tipped to join League One side Swindon, but appears to have opted for a move north of the border instead.
The Robins had held talks with Jones' agent and thought that they were in pole position to sign the midfielder.
However, with the player now rumoured to have undergone a medical at Hearts, Swindon's chief executive Nick Watkins believes that they may have missed out on their target.
"The player's agent seems to have gone to ground so we are still waiting to hear from him," Watkins told the Advertiser.
"We have heard he is having a medical in Scotland, though, so the manager and the chairman both believe he has slipped away."