The centre back has enjoyed a strong Football League career since signing as a trainee for Lincoln City in the early 1990's.
Carbon (pictured below) has since played regularly for Derby County, West Brom and Walsall - chalking-up transfer fees totalling over £1 million over a 13-year professional career.
And Thompson is hopeful that the uncompromising defender - who still owns property in Bestwood - will agree to join the Magpies in the near future, despite interest from other clubs.
"I am very much hoping he will join us in the next week. If we can get him in it offers competition to the squad."
It was widely-believed that Mike Edwards and new captain Alan White would form the partnership at the heart of the new-look Magpies rearguard.
But, with Thompson's central midfield options currently somewhat limited, the County boss is considering pushing Edwards forward into a midfield role he filled with mixed results for much of last season.
Carbon's potential arrival would allow him to do this and retain a strong back-line and, though the defender has attracted interest from other clubs within the Football League, Notts are now in a position to compete financially having handed the new boss one of the top three playing budgets in League Two.
As well as White and Edwards, new signing Matthew Somner and teenagers Tommy Hannigan and Bobby Wilson are the only other centre backs currently on the books.
Meanwhile, Thompson is also still hopeful that Sheffield Utd's Ian Ross could provide another way round his problems at the heart of the midfield.
19-year-old Ross is wanted on a long-term loan after impressing Thompson playing for Boston Utd last season.
And, despite Ross linking-up with the Blades for pre-season training, Thompson is hopeful that links between the two clubs could help him land the creative midfield player.
"Howard Wilkinson knows Neil (Warnock) and their Chairman very well, so we have very good connections that I am hoping will help persuade him to come to Notts County," said the Notts boss, who has signed 11 new players since his appointment in late-May.
Notts kick-off their pre-season campaign on Saturday at Hucknall Town, with just seven of the players who featured last year remaining in this all-new squad.
Kick-off is at 3pm with admission charged at £5.
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