The 30-year-old was hoping for a two-year deal - something the Magpies would be happy to offer him - and has now resigned himself to a move elsewhere.
"I am pretty certain I will be going elsewhere," Guinan told the Gloucestershire Echo.
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"There's a lot of managers away on holiday and I won't be making any announcement until I have spoken to everyone and made a decision."
Much-travelled Guinan scored 10 goals in the previous campaign, including a cracker against Notts.Thompson faces competition from a number of League Two clubs for the workmanlike striker, but the Magpies are now in a position to compete financially and would happily hand Guinan the two-year security he craves.
After signing four new players yesterday, Thompson has made public his desire to bring two more strikers to the club following the captures of Lawrie Dudfield and Jason Lee.
This could mean bad news for Steve Scoffham who, despite being invited back for pre-season by the new boss, doesn't seem to figure highly in his plans.
Scoffham, along with Lewis McMahon and Chris Palmer, is one of three existing Notts players who are waiting on a decision about their futures. Thompson though, isn't yet prepared to offer any of them a new deal.
Thompson is also set for talks with two full-backs in the upcoming week, as well as a creative midfield player.
For an in-depth look at Thompson's new signings, be sure to stay tuned to NCM.