Speaking less than an hour apart, Swansea's Paul Clement and Everton's Ronald Koeman said they hoped Sigurdsson's future would be sorted soon.
"I want it to be resolved as quickly as possible," said Clement.
"It's still close," said Koeman. "Soon is okay."
British media have reported that Everton have had two bids of 40 million pounds and 45 million pounds rejected for Sigurdsson, with Swansea holding out for 50 million pounds.
Clement confirmed that the 27-year-old, who did not go on the club's tour of America because of the speculation about his future, would not be involved in Swansea's Premier League opener at Southampton on Saturday.
"The way it is going there needs to be a compromise on both sides, normally when deals are done it is a win-win for both sides," said Clement.
Sigurdsson played a significant part in Swansea avoiding relegation last season, scoring 10 goals in all competitions and making 13 assists, the third best in the Premier League.
Koeman also said that his midfielder Ross Barkley, who has turned down a new contract and has been linked with a move to Tottenham Hotspur, is back in training.
"There is no offer on the table for Ross, that means he will stay at Everton," said Koeman.
"The player has a one-year contract and if there is no offer -- and maybe the club will not accept the offer because he is a good, young, English player. If somebody wants to buy Ross it's a big deal."
(Reporting by Neil Robinson; Editing by Toby Davis)
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