Wright-Phillips knows he will have limited chances at City this term and will be allowed to leave by manager Roberto Mancini. However, Bolton are unable to match Wright-Phillips' estimated £70,000-a-week wages and, so far, have been unable to find a way of bridging the gap.
"Shaun is a tremendous player," said Coyle. "He is someone I would love to bring to the club. Whether it is possible, only time will tell."
He added: "There are financial implications involved. Players at Manchester City are on contracts that are more than we could pay. There is a threshold we cannot go beyond.
"But there has been dialogue between our chairman and (City chief executive) Garry Cook. That is where we are at the moment. There is nothing concrete."
Coyle confirmed talks are further advanced with former Stoke striker Tuncay Sanli, who could be about to arrive on loan from Bundesliga outfit Wolfsburg.
"We are a good way down the line with that but it is not cut and dried," he said. "He is a terrific player, who really works his socks off."
As yet though, there has been no offer for Gary Cahill, who has been linked with a big-money move to Arsenal for much of the summer.
"I am surprised there has been no firm offer," said Coyle.
"Teams have had six or seven weeks already. I totally understand if they have made offers and talks are progressing, but why leave it until the last minute?"
Source: PA
Source: PA