Allardyce, 60, made his return to football on Friday, five months after being let go by West Ham United, having been appointed as the new Sunderland manager.
'Big Sam' is currently preparing for his first game against West Bromwich Albion this weekend, but he looks set to head in to that game without an assistant.
Allardyce's former Bolton assistant Phil Brown had been targeted for the role, but told the Southend Echo that he has rejected that opportunity.
Now, The Sun believe that Allardyce is now considering an approach for Steve Round, who is most well known for working as David Moyes' assistant at both Everton and Manchester United.
Round, 44, worked under Allardyce at Newcastle, and the ex-Premier League coach could reunite with the new Sunderland boss at the Stadium of Light.
With experience in the top flight, Round could be a smart appointment for Sunderland, with Allardyce seemingly approaching people he has worked with before having already missed out on Brown.