McDonald headed home the opening goal in the 1-1 draw after coming off the bench in the second half to take his tally for the season to 14.
Tony Mowbray's desire to refresh his squad has led to speculation that Celtic may sell McDonald in January to finance new signings, but agent Lou Sticca claims the 26-year-old is not keen on a move.
"I speak to Scott every day, and, as far as I am concerned, he wants to be at Celtic," Sticca told the Evening Times.
"I have also spoken regularly to Peter Lawwell, and he has told me that Celtic are happy with Scott.
"If anything does happen, it will be Celtic telling Scott to leave, not Scott asking to go."
Sticca refuted claims that Mowbray and McDonald, who has hit 64 goals in 128 games since moving from Motherwell, had a fall-out before the visit of Rangers.
"What we are seeing here is the usual reaction in the media if a club's top scorer is not playing," said Sticca.
"Scott is doing the business for Celtic, as his goals show."
Strachan has been linked with a move for several Celtic players, including Barry Robson, Gary Caldwell, Willo Flood and Mark Wilson.
Flood and Wilson have found first-team chances limited under Mowbray while Celtic could accept a cash offer for Caldwell given that talks over extending the defender's contract beyond the summer hit an impasse months ago.
Strachan is a big admirer of Robson, who he signed from Dundee United for around £1million, but the Scotland midfielder has been an integral part of Mowbray's team in recent weeks.
The former Celtic manager, who is reported to have held talks with Rangers striker Kris Boyd's agent, is desperate for additions to his injury-hit Middlesbrough side after winning just two of his first 11 matches in charge.
"We really need to do something," Strachan said. "We've got plenty of irons in the fire but it's about actually getting them.
"January is a difficult time to sign players because clubs are reluctant to sell.
"But I've never been on the phone so much in my life in football management."