I thought it was the opposite. I know Jason has said he was totally into The Police (and New Wave) when he was younger due to his dad's love of them. However, I do recall reading a story from Deborah , that Bonzo, Jason and Deborah met them backstage at one of their gigs and Sting was rather arrogant towards John which certainly...and obviously... disgruntled Deborah. Maybe that ended the love affair, but certainly when Roxanne came out John commented on how much he loved the song and how he knew they were going to be huge.
On a personal note, I was a big Police fan and had a big crush on Sting for sure. I have a photo somewhere where I am sat on a police motorcycle with my Police t-shirt on (I was 13 at the time...give me a break! )...I shall have to dig it out and post it for a laugh. I do look quite ridiculous