Gylfi Sigurdsson
Gylfi Sigurdsson is Everton's number one summer transfer target Getty Images

Gylfi Sigurdsson has rejoined his Swansea City teammates for the latter stages of pre-season training as Everton continue their prolonged attempts to make the want-away Icelandic playmaker the latest headline recruit of their lucrative summer spending spree.

Sigurdsson chose not to accompany the rest of the squad to the United States earlier this month for a tour comprised of three friendly matches, with the club confirming before departure that he "did not feel in the right frame of mind to travel due to the current uncertainty over his future".

The 27-year-old did play 45 minutes and even captain Swansea during a surprise 1-0 defeat at Barnet that took place the night before the team flew to Philadelphia.

However, he later remained in South Wales and trained with the Under-23s while Paul Clement's senior side continued their preparations for the new campaign with games against the Philadelphia Union, Richmond Kickers and North Carolina FC.

There had been a question over whether Sigurdsson would be welcomed back into the fold following Swansea's return to the United Kingdom or else continue with the youngsters or indeed on his own.

However, the former Reading, Hoffenheim and Tottenham Hotspur midfielder could clearly be seen taking part in senior training at the club's Fairwood base in a gallery published by swanseacity.com on Wednesday evening (26 July).

Such a development may hand Swansea supporters a sliver of renewed hope that Sigurdsson could yet stay at the Liberty Stadium, with Clement and owners Steve Kaplan and Jason Levien having yet to fully give up on that possibility.

Leicester City have also been battling hard to sign Sigurdsson, although it is Everton that have firmly established themselves as his leading suitor. The Toffees, who have already spent close to £100m ($131.3m) on seven senior signings during the current window to date, failed with an opening £40m bid a couple of weeks ago.

They recently saw an improved second offer worth a total of £45m rejected as Swansea hold firm on their £50m valuation of an influential player who only signed a new four-year contract in August 2016 before scoring nine goals and providing 13 assists to help the club escape the clutches of relegation.

"Of course we have interest in the player [Sigurdsson]," Everton manager Ronald Koeman, who is 100% sure that contract rebel Ross Barkley will leave his boyhood club over the coming weeks, said at a press conference held on Wednesday.

When asked if he would return with a third approach, he simply replied: "I don't know, I don't know."