Reports in Switzerland claim that West Ham have offered the 33-year-old a two-year contract with the option of a third year.
And Streller’s lawyer, Marco Balmelli, admits the former Switzerland international could be keen on a move having been at Basel for a second spell since 2007.
"It is true that West Ham have approached us,” Balmelli told Blick.
“Maybe Marco needs a new challenge again after seven years at FC Basel. It would be like a World Cup final for him."
Sam Allardyce has already bolstered his attacking options with the signings of Mauro Zarate and Enner Valencia this summer, although Andy Carroll has been ruled out for the rest of the year after requiring surgery on an ankle ligament injury and Valencia is likely to miss the start of the season.