The phrase "strong rumours" means there are widely spread beliefs or information flying around, suggesting that something is likely true or very likely to happen. Full definition
Oh btw, there are strong rumours suggesting that the phone will not come with a headphone jack but will include a single USB Type - C 3.1 port. (themrphone.com)
«It's a Premier League side with strong rumours of Tottenham. (whoframedruelfox.com)
There has been strong rumours about Xhaka being a done deal, but the player himself is saying that no offers have been made, to his knowledge and that he would like to know where he will be playing next season, before the Euro's kick off! (justarsenal.com)