Pattison is a free agent following a stint with Bidvest Wits in South Africa and is looking to return to the UK.
He has experience of English football after starting his career with Newcastle and also spending time with Norwich City.
The 27-year-old midfielder is now set to be given the chance to try and earn a contract with Bristol City, although he is still open to other offers at the current time.
His agent, Jonathan Hope, said: "Matty is raring to go and Bristol City have huge plans so we are hopeful of going in as soon as they return from their tour.
"He would definitely be a huge coup for the club should all go well.
“I believe in the player and (fellow agent) Tony Asghar and myself believe that Bristol City is where Matty would shine.
“However, he is still free and if an offer came in elsewhere we would have to look at this also."