He has also tested positive along with various members of their playing squad meaning the showpiece occasion against York City Knights is suddenly in doubt.
A decision will be made once the results of another round of PCR testing are received today.
Webster said: “We are hopeful it goes ahead. I am confident it will, seeing as the people who are getting tested again have already passed PCRs.
“That was only a couple of days ago, so I can’t see why they won’t again. I am really hopeful for everyone involved.
“As a coach I am doing everything I can – and so are the club and the RFL – so people get their day out in London.
“It has been a long time coming for both clubs so it’ll be fantastic if we get the game on.
“Some players are distraught they won’t be going, but we’ve had a real philosophy this year it is about team first. I’ve spoken to people and wished them well and there hasn’t been a lot of depression around the group.”
Featherstone’s last appearance at Wembley was for their famous shock Challenge Cup win over Hull in 1983 but Championship rivals York have only been once - when they lost to Halifax in 1931.
Although Super League has been decimated by Covid outbreaks in recent weeks, resulting in numerous games being called off, the second-tier has so far done well to largely avoid such issues.
The only game postponed this term was between Halifax and Sheffield Eagles in May due to a Covid outbreak at Sheffield.
Rovers were big favourites having won all 12 league games this term and given York have lost their last six matches.
Webster would not reveal which of his players are due to miss out but said: “We will scratch together a team.
“It has had a big impact on our team and I won’t be going, but I think we are still a strong team.
“We won’t be anything like the sides we’ve seen in the last month or two, but we’ve some really good players who haven’t had enough opportunity this year and they are going to get a go.”
If called off, the final will be rearranged at a venue in the north of England later in the year.