Boro have made three signings this summer, but accept that further additions are required if they are to remain competitive in the Championship.
Mowbray feels he is still lacking strength in depth and would like to bolster his striking options if possible before the transfer window slams shut.
He said in the Gazette: "My job is to try and identify footballers who can try to help the team. It's not my job to try to negotiate transfers so I don't know where that's at.
"I would hope we will have two or three players in in the next week or two which will freshen the team up to the point where it will create more competition."
Mowbray added: "We've been trying for a few weeks now and it's not easy when you haven't got a centre-forward on the bench who thinks he should be playing and is ready to rip his tracksuit off and come on and show you that he should have been starting.
"But hopefully we'll rectify that and create some competition in the next few weeks.
"We will try to strengthen in a few areas of the pitch before the window shuts. We've got two or three bids in for different players and we wait for those clubs to make decisions on their futures."