Clement, 45, took charge in January with Swansea in the relegation zone and guided them to a 15th-place finish.
Swansea City are reportedly in the pursuit of Louis van Gaal to take the reins at the Liberty Stadium after sacking Paul Clement.
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He added: "We felt we couldn't leave it any longer and needed to make a change to give the best chance of an uplift".
Jenkins praised Clement's role in helping keep the club in the English top flight last season.
Swansea may look to Welshman Tony Pulis, the Premier League's resident relegation avoiding specialist, in a bid to get them moving up the table. Koeman's stock remains high, particularly on the continent, and so Swansea will struggle to convince him - particularly when a quick turnaround is expected.
But talks never got going forcing them to appoint club legend Leon Britton as caretaker boss instead for tomorrow's crunch clash with Palace, despite only joining the coaching staff last month.
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A new manager coming in means Bartley must prove himself all over again, and his history at Swansea have shown it could flip either way.
Although the defender is settled at Swansea, the club's league position makes them vulnerable to bids from West Ham and other potential buyers.
He said: "It is not to say I wouldn't take it in the future, but I just think at this moment in time it is not the right move for me". The club are getting things so badly wrong and it simply comes down to the careless actions of Huw Jenkins and the rest of the former owners.
Bradley was the first American to manage in the Premier League, but his reign lasted only 11 games and 85 days.
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