Speaking with Swansea City's official website, Jenkins said: "It's a big thing for the club because he is a very important player for us".
The report claims Everton have tabled a £9m offer to Southampton to tempt them into selling the defender, who is under contract until 2018.
However, this time it does appear Williams would be open to the prospect of joining a club of the size and tradition of Everton and a move away from the Liberty Stadium, where he has given eight years of stellar service. Now, it seems, a bid has been made and accepted as Swansea seek to cash in on a 32 year old with two years left on his deal.
Although Williams is believed to be keen to work under Ronald Koeman, Swansea officially rejected Everton's £10million transfer bid.
"Delighted to have signed a new 4 year deal with @swansofficial".
Rumour Mill: our round-up of football gossip, rumours and speculationWith just two weeks to go until the beginning of the season, the Swans may be looking to hold on to their skipper for a little longer.
He has since scored 20 goals in 72 appearances for the club, with 11 of those strikes coming in 36 appearances last season as Francesco Guidolin's side finished an indifferent campaign 12th in the Premier League.
The Wolverhampton-born defender has not taken part in any pre-season matches having been given an extended break after captaining Wales to the semi-finals of Euro 2016.
Sigurdsson only reported back for club duty on Monday following Iceland's exploits in France, and he insists that Swansea continue to head in the right direction.
WalesOnline previously stated that the new USA investors in Swansea were going to make a new contract for Sigurdsson a priority.