The 21-year-old has become one of Europe's most sought-after defenders in the wake of an exceptional 12 months for both club and country.
As well as winning a second successive DFB-Pokal crown with RB Leipzig, Gvardiol was instrumental in Croatia's run to the 2022 World Cup semi-finals, playing every minute in Qatar and scoring in their third-placed playoff win over Morocco.
The former Dinamo Zagreb man ended the 2022-23 season with three goals from 41 games in a Leipzig jersey, while he also agreed a new deal with Die Roten Bullen until 2027 last September.
However, it remains to be seen how long Leipzig can retain Gvardiol's services for, as Man City are pushing hard to bring him to the Premier League in the coming weeks.
The Citizens are now believed to have agreed personal terms with Gvardiol, and according to Sky Deutschland, they have now approached Leipzig with an opening bid of €90m (£77.3m) including add-ons.
Gvardiol has apparently been identified as a "dream player" for Pep Guardiola, and transfer chiefs from City and Leipzig have been working on a deal for the past few days.
However, Leipzig are hoping to garner a world-record fee for a defender to let Gvardiol leave - an honour which is currently held by Harry Maguire, who was the subject of an £80m move from Leicester City to Manchester United in 2019.
Leipzig are understood to have inserted a €110m (£94.4m) release clause into Gvardiol's contract last term, but that option does not take effect until 2024, opening the door for a bidding war in the current transfer window.
While there is still no agreement between the two clubs, Man City have seemingly been handed a boost in their pursuit of Gvardiol, as Leipzig are already seeking out possible replacements.
Die Roten Bullen are apparently confident of agreeing a €30m (£25.8m) deal for Lyon's Castello Lukeba, while Lens' Kevin Danso, Southampton's Armel Bella-Kotchap and Wolfsburg's Micky van de Ven are also of interest.
Leipzig forked out just €18.8m (£16.1m) to sign Gvardiol from Dinamo Zagreb as a teenager in 2021, and the defender now has five goals and three assists to show from 87 games for the Bundesliga giants.
While Gvardiol has found fame as a centre-back, the 21-year-old has also been deployed on the left-hand side of defence during the early stages of his career, most notably for Croatia at Euro 2020.
Gvardiol could potentially touch down in Manchester as a replacement for fellow left-footed centre-back Aymeric Laporte, who continues to be linked with an exit after falling down the pecking order.
Laporte has apparently turned down the chance to join Tottenham Hotspur, but Aston Villa are now reported to have shown an interest in the Spain international.