Bates took over the captain's armband for the first time ahead of last weekend's 2-2 draw with Hull City, and is expected to skipper the side for a second time in this afternoon's game at Coventry.
David Wheater and Gary O'Neil have also carried out captaincy duties this season, but Mowbray is keen to start developing a relationship with a long-term skipper, who can be the bridge between the manager and his squad.
With question marks over Wheater and O'Neil's future once the transfer window reopens in January, Stocktonborn Bates looks to be the ideal candidate for the role.
I've been here for six games now, and there's already been three or four different captains, so it's something we have to sort out,
In an ideal world, we'd settle on one captain who was going to do the job long term.
Then I can develop a relationship with him and utilise him to get messages across to the team. If there are issues over discipline or whatever, I'll have a contact point to the team.
Every manager needs a player they can use to help convey their arguments to the squad. That's how I always captained football clubs. You're part of the dressing room and camaraderie, but you also have to have a more balanced approach.
In an ideal world, you have a captain who is, in every sense of the word, a captain of the club. I'll be talking to both Matthew and Gary about that in the next few days.
O'Neil could be a late addition to the squad for today's trip to the Ricoh Arena having returned to full training on Thursday, but like fellow injury victim Kevin Thomson, Mowbray is reluctant to rush the midfielder back into action.
As a result, Mickael Tavares is expected to retain his place at the heart of midfield, with Mowbray predicting the Senegal international, who is on a season-long loan from Hamburg, will be a valuable asset once he completes his adaptation to the pace and physicality of the English game.
His size, technique and ability mean all the attributes are there, said the Boro boss.
But he has to understand that the English game demands a really strong mentality because no one's going to be picking you up after they've knocked you over.
Mickael's come from German football and that's a methodical, pretty slowpaced game. It's closer to the Premier League than it is to the Championship. People will have their own view as to how well Mickael has adapted to that, but there is undoubtedly a period of adaptation required.
I think he's still going through that process, and I think he still finds some games extremely hectic. In Germany, every time he gets the ball, he has ten yards of space around him and he can pick a pass. In the Championship, you get the ball and there's five men jumping on top of you within a second.