Mr Coulson, 43, sued News International subsidiary News Group Newspapers over the construction of a clause within a severance agreement arising from his resignation in February 2007.
He asked Mr Justice Supperstone to grant a declaration that NGN, which stopped reimbursement in August, ''must pay the professional costs and expenses properly incurred'' by him ''in defending allegations of criminal conduct'' during his tenure.
Mr Coulson, who was arrested in July over the allegations and released on bail, has always denied any wrongdoing.
He resigned from his position as Prime Minister David Cameron's director of communications in January, saying that coverage of the scandal was making it too difficult for him to do his job.
Christopher Jeans QC, for NGN, said the clause covered the ''occupational hazards of being an editor'' and not alleged criminal activity.
''If we are wrong on that, we submit that the clause only operates in relation to proceedings and here there are none - no charge, no hearings. Also, there is no obligation to pay before the proceedings are over - and manifestly they are not.''
