Chelsea set a deadline of Friday at 17:00 BST for offers for Manchester City target Enzo Fernandez, who they value at £120m.
The potential move would see the Argentina midfielder link up again with new City boss Enzo Maresca, who was formerly his manager at Chelsea.
A potential deal for Fernandez relies on City selling Rodri, officially the best player at the 2026 World Cup among numerous other accolades, to Barcelona. City are not planning to sign Fernandez if he stays.
The defensive midfielder has been a crucial part of City's success in recent years, helping them win the 2022-23 Treble - including scoring the winner in the Champions League final against Inter Milan.
The 30-year-old has played 298 times, lifting a total of four league titles, plus several cups - and winning the Ballon d'Or.
Rodri wants to return to his native Spain and join Barcelona - with Real Madrid having dropped out of the chase - and City are asking for 80m euros (£68.4m).
But Barca's opening bid for a player out of contract next summer was only £38.5m.
BBC Sport's chief football news reporter Simon Stone says the Rodri and Fernandez deals happening are dependent on each other - but do not need to go through at the same time.
If City knew Rodri was going it would enable them to make a bid for Fernandez.
And it is possible he could even sign before Rodri is ready to play again after a minor back procedure.
Maresca is clearly a huge fan of Fernandez, having made him Chelsea captain when Reece James was injured.
And he played the Argentine in 79 of his 92 games in charge.
Fernandez is by nature a defensive midfielder - but Maresca played him further forward many times last season when Cole Palmer was injured - leading to him scoring a career-best 15 goals.
That means there are several places Fernandez could fit into Maresca's City team.
Read more about a potentially pivotal day here