Wilson returned to his first club in August on a contract until the end of January and he has made five appearances in all competitions this season.
McNamara has been pleased with the 29-year-old's impact and he is hoping to keep the right-back at Tannadice for the long term.
"I would like to offer Mark a new deal," said McNamara in the Daily Record. "He is a player I admire and that is why I brought him here.
"He has experience and been excellent for us. His calmness, knowledge and distribution have all been put to good use.
"Mark will help Keith Watson too because Keith has not really had competition in the right-back role.
"Mark has had a lot of problems with injuries in the past but he has not missed a day's training since coming here and has been great when called upon. I have had no problem with him at all and he is a great professional."
Wilson, who played for Celtic and Bristol City after first leaving United in 2006, is also keen to stay with the club.
He told the Dundee Courier: "I am contracted here to January but if everything is right I would love to stay longer.
"The big thing is that I keep playing. I need to stay in the team, be in the manager's plans and hopefully get a deal.
"Coming here the big thing was always going to be my fitness but injuries haven't been an issue. I haven't missed a day's training and it's important it stays that way until January."