Their first stop was Ukraine. A midfielder called Fred had piqued the interest of the Premier League champions and they wanted to bring him to Manchester. Unfortunately – or as its turned out, fortunately – so did their club's cross-city rivals and the Brazilian opted to join Manchester United.
No matter. Pep Guardiola had identified an alternative, a midfielder based in the south of Italy. City agreed with Napoli for Jorginho. The deal was done… but then it wasn't. Maurizio Sarri was appointed Chelsea manager and took the Italian schemer to Stamford Bridge.
“We tried,” Guardiola admitted. “But my advice for players is to go to the club they want. It would have been a mistake for us and for him if he came when he wanted to go with Maurizio.”
So City went into the 2018/19 campaign without a natural deputy for their ageing Brazilian midfielder. Their search continued, though, and the next stop on their European tour was Amsterdam.
Ajax, lovely Ajax, had honed the talents of a young Dutch midfielder: Frenkie de Jong. The 21-year-old could do it all and could play at centre-back for good measure. He was ideal.
You sense it was at this point that City started to lose patience. And that perhaps explains why their approach has become a little more aggressive. Every week, a new midfielder is linked with move to the Etihad Stadium.
A move for Atlético Madrid star Saúl Ñíguez was in the pipeline. Then his teammate Rodri was linked. Tanguy Ndombele is also an option. Declan Rice, too.
And this week City are supposedly weighing up a £52million bid for Benfica's Florentino Luís, a 19-year-old with just ten first-team appearances to his name.
It's not easy separating fact from fiction, especially when it comes to the transfer market. But moving for Florentino would, despite his hefty price tag, make sense for City.
Fernandinho will turn 34 years old next month yet there are no signs the Brazilian is slowing down. He has started 37 games in all competitions this term, completing 90 minutes in all but ten of those.
He, more than David Silva or Kevin De Bruyne, is the heartbeat of Guardiola's side, a midfielder who makes the transition from defence to attack appear seamless. When Fernandinho doesn't start, City are usually poorer for it.
And that is why being his deputy is not an easy gig. First-team chances will be limited, and when they are afforded the Brazilian's boots are not easy to fill. Florentino, however, could do so.
He may have only made ten appearances for Benfica's first-team but the Portuguese youngster has adapted to senior football with ease. Florentino is quick and agile across the ground – which enables him to swiftly halt opposition attacks – but can construct attacks from deep positions through intelligent passing.
When in possession, the teenager's upright yet languid style, coupled with his 6ft frame and long legs, make him reminiscent of Paul Pogba. It's a comparison that goes no further, though, given Florentino is more defensively minded and responsibility than the Manchester United star.
Given he has only played 490 minutes of football in the Primeira Liga for Benfica, it's difficult to gain a true reflection of his output because it's simply a too small a sample size.
For example, his interceptions attempted per 90 of 4.22 and tackles attempted per 90 of 4.95 are among the highest in the Portuguese top flight. Over the course of an entire season, they are unlikely to be sustainable.
Yet they do give a reflection of what Florentino could bring to the City side. He is an excellent destroyer but has the potential to become so much more than that at the Etihad.
Is he worth £52million? Almost certainly not. Could he become worth such a fee? Almost certainly. It's whether City are prepared to take that risk. And it doesn't always work out, as Bayern Munich have discovered with Renato Sanches.
Yet a season in which the youngster learns Guardiola's system and learns the demands placed upon Fernandinho could ensure Florentino picks up the mantle from the Brazilian when he no longer can perform week in, week out.
City have scoured Europe to find an heir for Fernandinho. Florentino may not be ready just yet but he could prove the man to end their search once and for all.