Die Son newspaper reports that the Stormers had signed Turner for the upcoming Super Rugby season.
However, Coetzee said Turner is just training with his team and has signed no contract.
"Matt just came to ask if he could join us for training. We've got no intentions at this stage (to sign him). There's no commitment from our side. He just wants to keep fit and train," Coetzee said at a press conference at WP's High Performance Centre on Tuesday.
Coetzee said they would look at the wings in their structures first before signing an outside player.
"There are a lot of other players in the system that we have to make sure that we give the opportunity first. But if Matt wants to come train, I'm not going to chase him away and say you're not welcome here. But there are players that we know are in the systems who we have to look at first... and he (Turner) understands that.
"There's no commitment from our side. It's not even been discussed. There's an entry level. He must go through club structures, through Vodacom Cup. That's how it is in the province. It's always been like that."
The 27-year-old Turner was born in Cape Town and attended Western Province Preparatory School before matriculating from Bishops.
He was one of the star performers in the 2006 Bishops team that was regarded by many as one of the best teams in the history of the school. Turner scored 25 tries at an average of more than one try per game during that season. He however did not make the Western Province Craven Week side that year.
He qualified to represent England according to the International Rugby Board's ancestry rules and regulations. Turner made the move to England and was selected for the England Sevens team for the first two legs of the 2009/10 World Sevens Series. He also played for the English Premiership club Bristol in the Aviva Premier League.
While on holiday in South Africa, Turner was released to play for the Southern Kings against the British and Irish Lions in 2009. He was also a member of the Springbok Under-20 team and Western Province Under-19 team.