Former Manchester City striker Benjani looks poised to join Blackburn.
Benjani, who is a free agent, has been training with the squad in the hope of cutting a deal.
Manager Sam Allardyce said: "We are trying to sign him on a contract because of his wealth of experience. He has trained with us a few days. He has shown us that we think he will be okay to play for us in the Premier League. So we are trying to sort something out."