The online poll of more than 4,000 people across England, Wales and Scotland found 82 per cent of football fans said they would not have a problem with an openly homosexual player at their club.
However, 8 per cent of football fans said they would stop watching their team.
Last week the Football Association chairman Greg Clarke told a Department for Culture, Media and Sport select committee an openly gay Premier League player would be subjected to “significant abuse” from supporters.
He said he would be cautious about advising a player to come out until homophobic abuse could be stamped out.
In the poll, commissioned by Afternoon Edition and carried out by ComRes, 71 per cent of football fans said clubs should do more to educate fans about homophobia.