The Sunday People says Birch and finance director Neil Robson are working frantically to broker a new package with the City.
A Leeds insider confirmed: "The club took on a massive responsibility when they were advanced £60m and now they are paying the price.
"It was ridiculous to take out a £60m bond over 25 years and agree to pay £90m in interest. It could yet see the club to the wall.''
Recent reports indicate Leighton has made the City a take-it-or-leave-it offer to restructure United's loans or face forcing them into administration.