Manager Gianfranco Zola chose his words carefully when speaking about Ashton's injury after training on Saturday ahead of Sunday's home game against Everton, which the visitors won 2-1.
Responding to a question about the striker he said there would be an update "soon" on his situation.
Ashton - who had surgery in the spring of 2009 - had been unable to take part in training, he said, as he worked on his personal fitness "while next steps were assessed".
Zola added: "When something like this happens, it is very much personal. Me as a manager I am here to make sure I can give him all the support he needs. I understand that it is quite a difficult time for him."
A day later, after the Everton match, Zola insisted nothing definite had been decided.
"Until someone tells me he is not going to make it, I am still confident he is going to come back," said the Italian.
"For the boy and for us we hope he will make it. I can't say more than that.
"Dean is working his way back on his own and with his own physio. I don't know when I will hear anything."
After arriving in east London at the start of 2006, Ashton helped West Ham to the FA Cup final four months later against Liverpool and scored in the 3-3 draw at the Millennium Stadium before his side lost on penalties.
ASHTON'S CLUB CAREER
Season, club, apps, goals
2000-05 Crewe 159 (61)
2005-06 Norwich 44 (17)
2006- West Ham 46 (15)
His performances that season earned him an England call-up for the friendly with Greece in August 2006, but he broke his ankle in training for that game and missed the whole of the 2006-07 season.
He came back to make 35 appearances, scoring 11 goals in the 2007-08 campaign.
In June 2008, Ashton signed a new five-year contract at Upton Park, when Alan Curbishley was manager, and earned an England cap under Fabio Capello, playing against Trinidad & Tobago.
A favourite with the Hammers fans, they were chanting his nickname 'Deano' again after he scored both goals in a 2-1 win over Wigan on the opening day of the 2008-09 season.
But in September 2008, in Zola's first training session after taking over from Curbishley, Ashton sprained his ankle and has not played since.
His injury situation has been another headache for Zola, whose team are third from bottom in the Premier League with 10 points from 12 games, in which they have scored a total of 16 goals.
The Italian is also without England striker Carlton Cole, who has a hamstring injury, leaving the club with no established Premier League forwards available for selection.
Against Everton, Zola partnered 20-year-old Zavon Hines with close-season recruit Guillermo Franco.
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