Jack Wilshere has held talks with West Ham about a potential move to the club, Sky sources understand.
Wilshere is available on a free transfer after he officially left Arsenal at the end of his contract on Saturday.
Sky Sports News has been told Fenerbahce are also interested in signing Wilshere.
The England international told Sky Sports News last week he was in no rush but was open to offers in the Premier League and abroad.
"This has been a good opportunity for me to rest and reflect on my life and what I want - I am not going to rush that decision," Wilshere said.
"The transfer window finishes early August, so we still have some time and with the World Cup still going on things happen after the World Cup and during.
"Everyone knows what Deadline Day is like, it's manic and teams start to panic so we will see. I am not putting a deadline on anything."
New West Ham manager Manuel Pellegrini took charge of his first training session with the club in Switzerland on Tuesday.
Among those taking part in the session were summer signings Ryan Fredericks and Issa Diop, who are starting their West Ham careers after joining from Fulham and Toulouse respectively.
New goalkeeper Lukasz Fabianski has not joined up with the squad yet after playing in the World Cup for Poland.