Last July about 1, 700 attended a pre-season friendly at home to Swansea City, but attendances for league games this season have ranged from 113 to 260.
Dawson picked up his injury during a pre-season game against Bournemouth and Redknapp is pessimistic about their chances of facing Liverpool on 16 August.
The former Crewe, Leicester, Birmingham and Blackburn midfielder took a break from pre-season training on Tuesday to talk to BBC Radio Stoke about his life, his football career and his hopes for the future.
"They have been professional about it and the fact that their manager and chief executive broke off from a pre-season training trip in Italy to come to Belfast showed their desire for Peter, " he added.