The Baggies returned to non-contact, small group training earlier this week and skipper Livermore is hopeful his team will get the chance to restart their campaign.
EFL clubs are set to vote on a framework which, if the Championship season did not resume, would see Albion promoted along with Leeds.
Livermore said: “The only fair way to finish it is on the field so there are no arguments.
“Every team is going to have their own agenda and ours is to finish the league and hopefully finish top.
“That is what we hope we are able to do. That is why we have been training on our own for the last seven weeks, for this opportunity.”
Livermore’s views echo those of Albion chief executive Mark Jenkins, who also outlined the club’s desire to finish the season earlier this week.
The Baggies sat second in the table, six points clear of third-placed Fulham with nine matches to play when the campaign was halted by the coronavirus.
Livermore insists the motivation among players to finish the job remains undimmed despite a break of more than two months.
He said: “I’m not sure there was any more motivation we could fit in. The boys from minute one this season have been flat out going for our goal.
“Despite living in such a strange time that has not changed. Our goal is to protect our families of course but work-wise we want promotion.
“The only way we can show our true appreciation is to finish it off properly and finish it off in style.
“If they can’t be there in the stadium then by all means we hope they are celebrating at home.
“We have a job to do in keeping the fans happy and entertaining fans. I don’t think there is any better way of doing that than getting back out on the field and finishing the job off properly.”
Livermore was also full of praise for the club’s coaching staff and science department for the programmes they put in place for players during the weeks away from the training ground.
He added: “It has been difficult because there is no set date on when we are back. Credit to the boys. Everyone has come back and looks like they are ready to go.
“Credit to everyone who worked on the training programmes because they have adapted to each player and have been pretty spot-on. You can tell that by the shape the boys have come back in.
“At the moment we’re not allowed at the training ground for long periods because of the numbers and we need to abide by the rules at all times.
“But it’s still nice to see the faces again. It’s a good group of friends and that’s why we’re all together in what we do.”