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Diamonds boss Garry Hill - currently on a family break - has already admitted that he wants to bring in a more experienced forward to partner Simeon Jackson, Michael Rankine or Lee Tomlin up front.
They seem to be favourites to secure Sills' signature after Blue Square Premier rivals Aldershot Town pulled out of a deal.
Stevenage Borough are thought to be in a head-to-head battle with Diamonds - although the Hertfordshire club have conceded defeat over a possible transfer.
Aldershot's assistant-manager Martin Kuhl accepted they had been priced out of a move to re-sign former fans' favourite Sills who was keen on a return to The Rec.
He said: "Unless the wage demands are sorted out, any deal for Tim is dead I'm afraid.
"I have been told that he is going somewhere else now and, while we were interested in bringing him back, we can't afford his wages.
"We would like to speak to him but we are so far away from each other in terms of wages that it is not something that's going to happen at the moment.
"Tim is a very good player and I'm sure there are a few clubs after him but we can't afford what he wants."
Stevenage chairman Phil Wallace added: "We've been unsuccessful in our attempt to sign a striker from a League Two club but we'll continue to look around."
Sills had a prolific spell at Aldershot but failed to find the net on a regular basis for Hereford last season following a free transfer - scoring twice in 43 first-team appearances.
The 6ft 2in striker - who has also played for Oxford United - was highly rated by Hereford boss Graham Turner.
However he has re-signed Steve Guinan from Cheltenham Town this week which could lead to Sills' exit soon.
If a deal is done, he would become Hill's sixth new signing and link up again with Gulliver.
Source: http://www.northantset.co.uk/sport?articleid=2953218