Speed was understood to be high on the Swans list last year when they were looking to fill the void left by Roberto Martinez, who left for Wigan Athletic.
The link for Speed tied in with the Swans looking to change their approach by opting against a third successive foreign manager, but they were linked with former West Ham boss Gianfranco Zola on Friday.
Zola's British assistant Steve Clarke was also linked but the attention has been on Speed who also fits the bill of Jenkins' desire for an ambitious young manager.
"Most of the young managers doing well happen to be British because they start off at those clubs," Jenkins told BBC Sport Wales.
"Most of the experienced foreign managers come in and take a lot of the jobs further up the ladder.
"The younger British manager in my own view has a lot to offer.
"Paul Trollope at Bristol Rovers, Terry Skiverton at Yeovil, Keith Hill at Rochdale and Eddie Howe at Bournemouth have all worked miracles on small budgets.
"Nigel Adkins has also worked miracles at Scunthorpe and has done a very good job and is very loyal to the club."
Swansea's last two managers have been foreign - Spaniard Roberto Martinez and his Portuguese successor Paulo Sousa, who quit for Leicester City on Sunday.
Goalkeeper Dorus de Vries looks to life without Paulo Sousa
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