According to the reliable X account Feyenoord Transfermarkt, the Dutch side have honoured a pre-agreed condition in Sterling's original deal by submitting a fresh proposal following the achievement of Champions League football.
"As a result of reaching the group stage of the Champions League, Feyenoord have honoured earlier agreements by making Sterling a new proposal. It is now up to Sterling to respond to this offer from Rotterdam."
The development is a notable reversal of the picture painted just three weeks ago, when reports from Algemeen Dagblad suggested the club had ruled out any extension. The Champions League clause appears to have changed the equation.
Sterling, 31, arrived in Rotterdam on a short-term deal in February after departing Chelsea by mutual consent in January. His time in the Netherlands has been limited: seven official appearances totalling 349 minutes, with just one assist to show for it.
The former Manchester City and England winger was valued at £160 million at the peak of his career. Transfermarkt currently place him at €5 million.
Dutch television pundit Johan Derksen was blunt on the subject when it emerged Tuesday evening.
"There is no reason whatsoever to keep an expensive player like Sterling here. He adds absolutely nothing to Feyenoord. You'd be better off giving an 18-year-old a chance."
Whether Sterling opts to stay will depend on the terms on offer and what other interest exists this summer. At 31 and with a limited recent record, the options available to him will shape his response.