The Blues will now discuss personal terms and a long-term contract, with permission to arrange a medical ahead of a move to Stamford Bridge.
The 20-year-old London-born attacker could tip Chelsea’s spending beyond £150m in January alone, taking this season’s spree past £450m.
The England Under-21 international has only played nine times for his club but scored twice after spending significant time out with an ankle injury.
Madueke can play on either wing, but the left-footed attack prefers to play from the right.
If the talks are finalised, it will be the Blues’ 15th major signing of the season and sixth this month.
Chelsea will hope he can improve a run of form that has seen the team win just one of their last 10 games, leaving the club 10th in the Premier League and 10 points behind fourth-placed Newcastle.