Rovers have already brought in nine players this summer while talks with further transfer targets are ongoing.
"In an ideal world I'd love to get in three or four new faces, I really would," Bowyer told the Lancashire Telegraph. "It's constantly ongoing and will be until the end of the transfer window.
"It's still ongoing," he said about Bannan. "These things take a little bit longer than managers want. We've just got to keep working hard at it and try to get things over the line."
UAE international midfielder Amer Abdulrahman has also been training with the club but is expected to return home in a couple of days time.