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It's a position that Rovers had already looked at in the summer, with deals for Brian de Keersmacker and Reo Hatate breaking down on deadline day.
The team has coped quite well without them but a long-term hip injury for Adam Forshaw has left them a man light.
On top of that, the absence of Morsy at the weekend showed the importance of adding another experienced midfielder. The free agent signing has performed brilliantly but at 35, is not someone the club wants to rely too heavily on.
Kristi Montgomery is developing fantastically well but Saturday proved both he and Moussa Baradji benefit from a guiding figure alongside them.
"We've talked about positional stuff and I think that's very much an area where we can create competition for places," Mowbray told Lancashire Telegraph.
"I'm sure we've got a department looking and I think within the next week or so I'll be shown some players.
"Ultimately, they have to fit within the financial restraints of the football club.
"It's no good going and picking a £10 million footballer that I think he's coming and we can pay him his massive salary.
"It's not going to happen; we've got to pick players that we feel can help this team within the structure that we've got and I'm just part of the process."
(Image: CameraSport - Dave Howarth)
Morsy's impact at Ewood Park has been obvious. With Sondre Tronstad departing, he has stepped into that role and has played a key part in Montgomery's development too.
He returns from suspension against Stoke City and is likely to slot straight into the midfield.
"Sam is an influence on the players around him," Mowbray admitted.
"It's a fire that has to burn in your belly and you need an instinct to win. Win your individual duels; when the balance of the game is flowing the wrong way, you have to turn it around with your personality on the pitch.
"Sam definitely has that. He is not Lionel Messi, he's a destructive, intelligent footballer with an opinion and a voice.
"He's allowed to express himself on the field without going rogue and helping people understand their roles."