Coyle feels the Bolton-Tottenham clash on Wednesday could present a "wonderful opportunity" for Muamba to thank fans and players from both clubs for their support following the midfielder's cardiac arrest last month.
"We have always said that before the end of the season, we would love it if Fabrice was fit and available to come to a game," Coyle said.
"We have to remember after everything he has been through, it has to be the right thing for him, his family and the medical team.
"But it is an open invitation, and if Fabrice is fit and well for that then I think the game against Tottenham would be a great opportunity, because of the events that took place at White Hart Lane.
"It would give a chance for everybody to see how well he is doing and from his end, it would also give him a chance to thank both sets of fans, who were magnificent on the night, and the Tottenham players - he has already been touching base with our players - because the concern they showed for Fabrice that night was remarkable.
"If it came about, I think it would be a wonderful opportunity.
"We are always speaking to him and we will do that again between today and tomorrow.
"If the family and Fabrice think it is something he would like to do, he would be welcomed with open arms."