With their rebirth under David Moyes, West Ham are pleased and hope to reward him at the end of the season with a new deal, The Guardian claim.
The Hammers hope that in May the picture will be clearer.
West Ham may already have given new terms to Moyes under normal circumstances.
The financial effect of the pandemic, however, suggests that they are uncertain of what the former Everton boss will be willing to give to start talks now.
West Ham lies seventh after staying up last season, two points behind fourth-placed Liverpool.
And senior West Ham figures agree that not keeping Moyes, who returned for a second spell after replacing Pellegrini in December 2019, was a mistake.
