The 22-year-old Dundee United striker has been heavily linked with a move to Blackburn after the Scottish champions failed with a previous bid for the player, who has been valued at £2million by United.
McCoist - who picked up his first win as Rangers manager thanks to a 2-0 victory away to St Johnstone - is keen to strengthen his squad further and confirmed that Goodwillie was still a target.
He said: "I don't think he's a Blackburn player. He is a player we have made no secret about but he is still a Dundee United player and we have to show them a lot of respect.
"What I would say is, if we had an opportunity to bring David Goodwillie to Rangers, then I would like to take that."
Responding to reports that Rangers have submitted a fresh bid for Goodwillie, McCoist added: "I don't know if it's accurate in terms of a fresh bid going in but I know our people have been talking to their people."
Den Haag's Wesley Verhoek also remains on McCoist's radar and the Ibrox boss said: "That's something we wouldn't rule out. He is a player we have watched and who we like.
"The first bid went in eight or nine days ago. There is an opportunity that could possibly happen but we haven't taken it any further yet."
He added: "I'm very keen on the fact that people are keen on coming to Rangers.
"That might be an obvious thing to say but I don't mean it to sound obvious - I think it's a very important thing.
"I would never want to undermine or under-sell our club because it's a massive club and it should be a club that people want to play for."
Goals from Steven Naismith and Nikica Jelavic secured victory over Saints in the Clydesdale Bank Premier League after Rangers had been held to a 1-1 draw by Hearts last week and then suffered a midweek defeat to Malmo in their Champions League qualifier.
McCoist said: "I was really pleased. We spoke before the game about starting the game better than we did in the previous two games.
"We did that and we were sharper and stronger and we were more direct in the opening period. We were very positive.
"I was pleased with the chances we created, we scored two goals and could have scored more.
"We still have a long, long way to go but we have taken a small step in the right direction. I don't know about relief, I was just more pleased for the boys than anything else."
Saints boss Derek McInnes felt there were positives to take from the game despite ending up empty-handed.
He said: "Once a team like Rangers get their noses in front, they get a lift confidence-wise, although it has been pretty clear that they have been striving for that confidence. It makes our task of getting back into the game that bit more difficult.
"Once we lost the second goal, it was a real uphill task and I think some of the players lost a wee bit of heart and it was always going to be very difficult for us.
"There are still some positives to take from the game and I've no doubt we will improve and get better as we go along."