"It is a very sensitive situation so if I am offered the job and I accept it I'll have mixed emotions," the former Fulham, Real Sociedad, Coventry City and Larissa manager told Sky Sports television on Sunday.
"I'm torn really because if I end up doing the job I'll be very happy but ideally I wouldn't be doing the job because one of my best friends would still be doing the job. And he's not here now," said the 41-year-old.
"My feelings are mixed but I am a professional and someone's got to do it. So providing everything goes well and I get the opportunity to do it, then I will give it my best shot."
Speed was found hanged in an apparent suicide at his home in north-west England in November, aged 42. Police said there were no suspicious circumstances.
Although Wales were eliminated from the race for the 2012 European Championships, they had won their last three internationals and were showing signs of real improvement under Speed's guidance.
Their next match will be memorial for Speed against Costa Rica at Cardiff City's stadium on February 29.
Coleman said, however, that he would not consider it appropriate for him to be on the bench at that game, if appointed, although he would be present.
"Personally I don't think it's right for me to take that game," he said. "I think it's for the people who are already there, it's a tribute to Gary, and I'll watch from a distance."
Former Wales striker John Hartson is the only other candidate to have publicly stated an interest in the position but he said Coleman looked the favourite.
"The word on the street we're all hearing is that he [Coleman] will be appointed this week and good luck to him," he told the BBC.
