McNamara, who spent a decade as a player at Parkhead, is thought to be among the contenders to replace Neil Lennon after the Northern Irishman resigned yesterday.
The former full-back is still relatively inexperienced as manager having started out just three years ago but his impressive achievements at Partick Thistle, who he took to the brink of promotion from the Scottish first divisions, and then United, who he led to last weekend's William Hill Scottish Cup final, mean he is already highly regarded.
Robertson, though, hopes McNamara will stay at Tannadice to finish the work he has started. "There are going to be rumours that he is going to be linked with Celtic but I think he is happy at United and not finished there," said the defender. "I can understand 100% [why he would be linked with the Celtic job]. His style of play is very modern. By getting the ball down and playing we have attracted plaudits for our way of football.
"But I believe there is still more to come from him and there is still more to come from us. I think that he has had a good season and everyone is looking at his style of play. Personally, he has done a lot for me. I still think, though, that he has unfinished business at United, as do we players after the cup final defeat. Hopefully, he doesn't leave and hopefully none of the boys leave either.
"Could he end up up at Celtic one day? Who knows? All I know is that he is the United manager and will continue to be. I think he could easily be ready for a bigger club but he is unfinished at United. He has a good group behind him."
Robertson only signed for United last summer but believes he has improved under McNamara over the past season. "It is his knowledge of the game [that impresses me the most]," added the 20 year-old who has been linked with a move to Everton. "He has been in football so long and he can pass on his experience to all the players, but especially so to me and the other full-backs because that was his position for 12 years at the highest level. You also have to consider his style of play as he doesn't like the team to just lump it up the park and play off second balls. I think that's the right way to play.
"It was really our first full season together and we finished fourth and got to a cup final. Maybe we will look back on that as a success but it is hard to do so just now. If we can all stick together then there will be more to come from us next season."
Regardless of who becomes the next Celtic manager, Robertson hopes United would be in a position to push them closer next year. "No doubt there will be ins and outs at Celtic, as there always are. Our aim, though, is to close the gap on them. They ran away with the league again this season while we finished fourth but if we can push for second then who knows how close we can get to them."
Robertson was at Airdrie's Excelsior Stadium to promote the Bank of Scotland Midnight League West Regional Finals