The champions fell nine points behind Liverpool following a 3-1 defeat at Anfield on Sunday.
Former City captain Kompany departed the Etihad Stadium last season after leading them to the title but the champions opted not to replace him.
Manchester City find themselves in the midst of a defensive injury crisis after Aymeric Laporte suffered a long-term knee injury, while John Stones and Nicolas Otamendi have all been sidelined at various points this term.
Defensive midfielder Fernandinho has been deployed as a makeshift centre back recently but Kompany does not believe defensive panic-buys in January will be the solution to Pep Guardiola’s problems.
"I don't think they need to sign another defender," he told Sky Sports.
"We always struggle at Anfield. I said that on Super Sunday: you're fighting 25 years of not winning at Anfield and that's difficult, it's two games in one game - you're playing a great team and you're fighting history.
"Flip it around and the same will happen for Liverpool - they will fight the history of not winning the league for 30 years.
"That should be to City's advantage I still think. As to the defence, the best way for City to defend in the past has been to attack. They have no reason to change that.
"As soon as they start reconnecting with the best performances, I'm convinced that we can see a sustainable amount of wins."
