The Eagles revealed on Boxing Day that boss Vieira had tested positive for Covid-19.
Vieira has missed the club’s last two matches after it was revealed on Boxing Day he had tested positive for Covid-19.
While the Eagles only confirmed the news five days ago, Roberts hinted on Friday that the 45-year-old could finish his period of isolation in time to be at Selhurst Park for the New Year’s Day fixture.
“Patrick is very well,” the Welshman said. “He has recovered well this week so crossed fingers we will wait and see what happens, but hopefully he will be with us very, very soon.
“On a day-to-day basis we are being tested, so we will wait and see what tomorrow morning brings.”
Asked if Vieira could be on the touchline this weekend, Roberts admitted: “It is a possibility and obviously from our viewpoint we want him here.
“We have desperately been hoping he will be back at the helm so we are waiting to see what today, tonight and tomorrow will bring in terms of news.”
Palace were able to cope impressively without Vieira on Tuesday when they claimed a 3-0 win at home to Norwich which saw them end 2021 in 11th position.
Nathaniel Clyne, Conor Gallagher, Michael Olise and Ebere Eze were also absent for unspecified reasons while Wilfried Zaha was suspended, but the latter is set to feature against West Ham.
It will be Ivory Coast winger Zaha’s last match before he departs to take part in the African Cup of Nations, with club colleagues Cheikhou Kouyate and Jordan Ayew also in action for their respective nations of Senegal and Ghana at the tournament which begins on January 9.
Roberts, who has previously spent time as technical director of the Moroccan Football Federation, added: “We wish them all well in the AFCON. It is a really important tournament.
“We knew of course this situation would arise at this time of the season.
“They are three important players we are going to miss over the next few weeks but being fully aware of that we feel we have players who can step in and take their opportunity, like JP Mateta did a couple of days ago.
“It is important when players get their opportunity, they step up.”
Team selection for Palace will again be dictated by the results of their routine PCR testing which took place on Friday, but Joachim Andersen is expected to feature despite his late withdrawal against Norwich.
James McArthur remains unavailable with a hamstring injury.
“In terms of availability, I think we are in a fairly good place,” Roberts explained. “Who knows what today brings in terms of the PCR process. We will take that as we do every day of the week and adapt accordingly.
“There is competition for places with one or two players stepping in and making a case for staying in the team. Patrick will select a starting line-up tomorrow and he will leave that as late as possible.”