Fekir is expected to become the Reds' next signing of the summer following their £40 million capture of Monaco midfielder Fabinho on Monday.
"I'm not going to tell you it's going to happen on a very short basis but it should because it seems quite obvious from the Lyon camp and the Fekir camp, Liverpool is really the first choice".
Maddock added that Aulas is open to the 24-year-old leaving the club but could stretch out negotiations until after the World Cup, when Fekir's value may have increased depending on how he performs in Russian Federation.
The Brazilian, whose deal will begin on 1 July, said the club's infrastructure looked "exceptional". "I will try to create my own history at this football club".
"He has ability and mentality to play at the highest level in a number of positions".
Lyon would also prefer to wait until the World Cup is over as they believe Fekir's fee could be boosted again by his performances.
Fekir had an outstanding season in 2017/18, scoring 18 goals and tabling six assists in Ligue 1.
Fabinho spent two seasons on loan at Monaco from Portuguese club Rio Ave before making a permanent move to the principality in May 2015.
He's more than comfortable operating at right-back though, the position he originated in. With plenty of the transfer window left, we can see Liverpool building a strong squad and compete for the Premier League title. He also has four caps for his national side.
Lyon's skipper and influential playmaker wants all negotiations concluded in the next week and a half to ensure he is able to focus on his World Cup campaign with France.
Liverpool made an initial payment of £39.4million, with add-ons worth £4.3million being triggered around objectives such as qualifying for the Champions League.
Fabinho has played four times for Brazil but failed to make their squad for the upcoming World Cup in Russian Federation.
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