Ibrox side Glasgow Rangers finished 39 points behind their Old Firm rivals last season.
Benni McCarthy has told BBC Scotland that Rangers will compete with Celtic next season if more signings like Bruno Alves are made.
The 35-year-old joined Rangers on a two-year deal earlier this week, becoming Pedro Caixinha’s first signing as the club’s manager.
Alves, who has won 89 caps for Portugal and picked up a winners medal for their Euro 2016 triumph last summer, should add a sense of solidity to a Gers defence which looked more than erratic at times under Mark Warburton last term.
The Ibrox side finished third on their return to the Scottish Premiership, 39 points behind Celtic who won the treble without losing a domestic match, and it is clear that Caixinha has a lot of work to do in order to bridge that gap.
McCarthy was at Porto when Alves was breaking through and although the former Blackburn Rovers striker does not believe that signing his old team-mate will cause a power shift in Glasgow, he does claim that several more arrivals of the same calibre would push the Hoops next term.
Asked by BBC Scotland if Alves’s arrival is enough to bridge the gap between both Old Firm sides, McCarthy said: “I’m not too sure he’ll be able to change that because Celtic are so strong.
“It’s going to take more than one Bruno Alves in that Rangers side to take the title from Celtic, but if they sign a couple more players like Bruno, then I think Rangers are in with a shout of giving Celtic a run for their money.”
Receive exclusive football transfer news and updates twice a week to your mailbox
