Birmingham manager Alex McLeish admitted he had made an enquiry about Aiden McGeady but has cooled his interest after being told the player is not for sale.
And Wigan's Roberto Martinez confirmed he failed in a bid to take Scott McDonald on loan until the end of the season with a view to a permanent deal.
Strachan, who has been linked with Gary Caldwell, Stephen McManus, Barry Robson, Mark Wilson, Willo Flood and McDonald, as well as Rangers striker Kris Boyd, is giving nothing away about the names on his wish-list.
He said: "We are trying hard to bring in people who can lead and people who want to be led.
"I want to bring in leaders and men - that's hugely important now. I have to have people who I know, players I know who are men, who are leaders, and who know about playing at this level.
"There will not be any foreigners coming in this time, that's for sure. We have to add that wee bit of enthusiasm and knowledge."
Reports north of the border have suggested Caldwell, Robson and Flood were the main focus of discussions between the two clubs earlier this week as Boro attempt to re-shape their squad on a tight budget.
However, Strachan knows he may have to remain patient as he attempts to get his men.
He said: "Everyone plays games and wants to get the best deal they can for their club. It's brinkmanship - we will see how it goes."
McLeish said of his attempt to land winger McGeady: "We have made enquiries for several players. I am not going to confirm or deny any names.
"But as regards Aiden McGeady, we made an enquiry but we were told he is not for sale. The situation won't change until someone says he is up for sale."
Martinez claimed he did not have the funds to complete an instant deal this month for McDonald, who has netted 64 goals in 128 games since signing from Motherwell.
Martinez is in need of reinforcements up front to ease the burden on Hugo Rodallega, with £2million summer signing Jason Scotland yet to score, and admits he is an admirer of McDonald.
"We are in the January window and we need to strengthen the squad, that is no big secret," said the Spaniard, who attended Sunday's Old Firm derby.
"Scott McDonald is a great goalscorer and has a great record in the Scottish game, has played European football and is an attractive player for any team in the Premier League.
"But I'm not going to go into detail on any names; we are going to be linked with many names, I understand that.
"We have been following many players and the key now is to bring in the right characters."
Of his presence at the Old Firm clash Martinez said: "I love watching games - I don't watch enough football - and to see an Old Firm derby is always a great atmosphere."
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