Also on Jenkins's list of young managers who have succeeded on limited budgets is Scunthorpe United boss Nigel Adkins.
He has achieved two promotions at Glanford Park and kept the Iron in the Championship last season, while operating on a budget that was not just the lowest in the division but also thought to be lower than several clubs in League One.
It is understood his chairman Steve Wharton has not received an approach from Swansea.
The same goes for Rochdale chairman Chris Dunphy who is away with the club on their pre-season training camp in Spain where manager Keith Hill is also present.
Hill took Rochdale out of the bottom tier of the Football League for the first time in 37 years, gaining automatic promotion having endured play-off heartache the previous two seasons.
Bristol Rovers boss Paul Trollope and Yeovil's Terry Skiverton are other names mentioned by Jenkins as possible contenders, but he could plump for another option altogether.
That is unlikely to be Brighton manager Gus Poyet though, the man who was widely believed to have been beaten to the job by Sousa last summer.
Seagulls managing director Ken Brown said: "There's been no contact from Swansea and if there was it would be a very firm 'no'.
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