Ibrox side Glasgow Rangers are hoping to stop Celtic from winning a sixth Scottish Premiership title.
Rangers have been busy adding players to their squad this summer, with nine new arrivals heading to Ibrox so far.
Rangers have brought in the likes of Niko Kranjcar and Joey Barton, and they have made no secret of their desire to end Celtic’s dominance over the Scottish Premiership.
However, Walker believes that Mark Warburton’s side could be frustrated in their first season back in the top tier, and he has backed Aberdeen to finish ahead of them.
"Much can happen between now and the end of the transfer window but as things stand, my guess is that Celtic will improve under Brendan Rodgers and retain the title for the sixth season in a row," he said. "I can see Aberdeen holding off the challenge of Rangers to again finish second with Mark Warburton`s men third."
Celtic have won the last five Scottish Premiership titles, and they remain the bookies’ favourites to be successful again this term.
The Bhoys’ appointment of Brendan Rodgers has increased optimism around Parkhead heading into the new campaign.
Rangers, meanwhile, have started their season by winning their first four competitive games in the Scottish League Cup.
Rangers start their season with a match against Hamilton, while Celtic take on Hearts first.