The firm has used Consolidated Communications for the past eight years but has opted to refresh its PR handling by putting the business out to pitch.
Consolidated director Will Holt said that although the agency had been invited to repitch for the business, it had declined as it 'felt it was time for a change'.
Blockbuster communications manager Tim Fairs confirmed that it was the first time the account had been reviewed in the eight years Consolidated had held the brief.
'It's not that Consolidated has done anything wrong. These reviews normally take place every two to three years so we felt it was time we reviewed the account,' he said.
'Our business is becoming more proactive in terms of PR and cause-related marketing, and it's about time we saw what's out there,' Fairs added.
It is understood that at least three other consumer agencies are to pitch for the account, worth a 'sizeable' six-figure sum.
The outcome of the review is expected next month.
In April the firm's UK arm announced plans for a tie-in with supermarket chain Sainsbury's, while a review of its TV advertising account was conducted in March.
The chain employs in excess of 89,000 employees worldwide, and earlier this week opened its 8,000th store - in Sao Paulo, Brazil.