Rotherham United chairman Tony Stewart says he believes there are 15 clubs in League One which will vote to end the season when they meet on Tuesday.
Clubs will vote on a framework approved by the EFL board which includes keeping promotion, relegation and play-offs.
League One clubs remain undecided while League Two clubs have indicated that they wish to end the current season.
"The consensus we get is there is no desire to complete the fixtures," Stewart said.
"We believe about 15 clubs would vote against carrying on."
Prior to the suspension of football in March due to the coronavirus pandemic, Rotherham were second in the League One table with nine games still to play.
In May at least six League One clubs including Sunderland, Portsmouth and Ipswich said they wanted the season to continue, though 12 votes are needed for any decision to go through.
Meanwhile, the Championship has set a provisional restart date of 20 June, with teams already back in training.
"I don't think for one minute the team that is fourth bottom, just out of the relegation positions, is going to want to continue and the teams right up to 10th will feel the same," Stewart added.
"The fact is it is going to cost us £150,000 to do the testing and you have to bring people out of furlough."
'It's been dragging on'
While the EFL board "unanimously agreed" upon their recommended framework for how the season could be completed, they will also review ideas submitted by clubs.
League One strugglers Tranmere highlighted an alternative plan last month which they say is based on "statistical analysis of points per game going back three years".
Rochdale boss Brian Barry Murphy, whose side are 19th in League One and four points off the relegation places, has called on EFL clubs to make a swift decision on how to go forward when the vote takes place, amid concerns over when and how the 2020-21 season will be played.
"It's been dragging on quite a long time," he told BBC Radio Manchester on Thursday.
"The big problem is that every single club in the country will have a different agenda depending on where they are in the league or what their personal circumstances are.
"My personal opinion is that there isn't anything new that hasn't been there for the past two or three weeks and it's time for the EFL to just make a decision and give everyone in our league a sense of clarity about what are their plans going forward and, even more importantly, what are their plans for next season? Because that is going to be very important."