LONDON—Britain’s Conservative Party says a former News of the World executive may have given the prime minister’s former communications chief advice before the 2010 national election.

The Conservative Party said Neil Wallis, who was arrested last week in Britain’s phone hacking scandal, “may have provided Andy Coulson with some informal advice on a voluntary basis before the election.”

Coulson resigned from his post as Prime Minister David Cameron’s communications chief in January amid allegations that Coulson was aware of phone hacking when he was editor of the News of the World tabloid. Coulson, who denies wrongdoing, was arrested this month in the phone hacking scandal.

The Conservatives said neither Cameron nor any senior members of its campaign team were aware of the relationship until this week.