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Pep Guardiola's side have had an up and down season, as everyone has pretty much, but the former Premier League champions have only lost twice and their form is greatly improved.
With Liverpool's recent issues, many believe that Guardiola's side will end up as champions, even with local rivals Manchester United currently above them in the league.
Despite winning six league games in-a-row, scoring 15 goals, City are lacking upfront due to the form, and injuries, of Sergio Aguero and, to a lesser extent, Gabriel Jesus.
They could do with another option in attack and Richards thinks the addition of Costa, recently released by Atletico Madrid, would win them the league.
"Manchester City are already on a ridiculously good run of form but if they signed Diego Costa now, he would win them the Premier League - I am sure of it," the former England full back wrote in his BBC Sport column.
"Costa is 32 and I am not suggesting he is a long-term solution for City up front, but the former Chelsea striker is a free agent after ending his Atletico Madrid contract in December, and can sign for anyone for nothing.
"Why not get him in until the end of the season? He would do more than just ruffle a few feathers and be a pain in the backside for opposition defences - he is a proven finisher who would offer Pep Guardiola's side a proper plan B.
"Yes, you would have to cover Costa's wages, but the massive difference he could make to City's season would make that worthwhile."
The 32-year-old Spaniard did win the Premier League twice with Chelsea during his previous spell in England, scoring 52 goals in 89 league appearances, but his form has been lacking recently.
His return to Atleti didn't go according to plan and he scored just 12 times in 61 appearances in three years back at the club where he built his reputation.
Diego Simeone brought in Luis Suarez last summer, teasing the possibility of a proper sh*thouse forward line with Costa, but the Uruguayan took centre stage.
Atleti hoped to sell Costa and sign Edinson Cavani but they couldn't afford both wages so the former PSG man went to Manchester United instead.
On Jesus, Richards added, "I like Jesus a lot, and he is far more than just a grafter, but when I watch him he is not always looking to get on the end of balls into the box like he did against Cheltenham in the FA Cup on Saturday - he is often lurking deeper or on the left, linking play.
"It means City sometimes don't have a focal point. If they had someone who constantly wanted to run in behind defences then, with their creative players looking for them, I honestly think they would be frightening. They would clean up, no matter how teams tried to stop them.
"Costa could be that striker and not only would he finish the chances that City are making, his presence would increase the opportunities for his team-mates too."
Do you think Costa would work at City? Let us know your thoughts in the comments.
Featured Image Credit: PA
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