Wright, who is out of contract with Sunderland,has been training with the Sky Blues for 2½ weeks and Coleman has been impressed enough to want to talk about a contract.
Coleman said, "I will be speaking to Stephen because I would like to keep him here. He has done well for us, he is an out-and-out right-back and a free agent. He has been with us for two weeks and we like him, we hope he likes us and I will be speaking to him about taking it further."
Now that David McNamee has left the club, Wright would be an ideal replacement.
Chris Coleman has told how McNamee brought an end to his two-year injury nightmare at the club.
"I talked to Dave at the end of last season because he missed a lot of football with a recurring hamstring injury," he said. "Ability wise he is not a problem, but I needed to see that he was able to sustain a level of fitness in training because we couldn't afford to have him for five months of the season and then injured for four months. Everyone has injuries and it was through no fault of Dave's, and sometimes that is just the way it works. But I want a squad of players who are fit rather on the treatment table, which is what we had a lot of last year."
"I explained to David that if he got through the pre-season and played some games, if his fitness was good, then he would get a contract with us. But I think David wanted a contract sooner rather than later because he wanted to look after himself with a bit of security.
"Plymouth have offered him a good contract but I wasn't prepared to do that until I was 100 per cent certain of his fitness. He is a free agent and has taken up that option at Plymouth and there are no hard feelings."