Arsenal will reportedly have to pay Real Madrid €90million (£77m) if they want to complete a deal for Rodrygo this summer.
The Brazilian winger appeared destined to leave the Bernabeu after telling Madrid that he never wanted to play for them again before choosing not to play in El Clasico against Barcelona in May.
The 24-year-old felt that he was in the shadow of superstar team-mates Kylian Mbappe, Vinicius Jr and Jude Bellingham and saw his role depleted towards the end of the season, as he frequently was left on the bench under Carlo Ancelotti.
However, a summer move has appeared less certain since Xabi Alonso's arrival, with Rodrygo said to have impressed his new boss in training.
But Arsenal remain intensely linked with the forward, who has reportedly been handed no guarantees that he will feature in Alonso's long-term plans.
And Real Madrid have set their asking price at €90m, according to Spanish outlet Cadena SER, who claim there is 'a real possibility' of Arsenal completing a deal.
Rodrygo was benched by Xabi Alonso despite assisting Madrid's only goal against Al-Hilal
Arsenal will reportedly have to pay Real Madrid £77m if they want to to sign Madrid's Rodrygo
Xabi Alonso claimed his first victory at Real Madrid boss after beating Pachuca 3-1 on Saturday
They also report that Rodrygo wants to 'explore other options' than the Gunners because he is aware of interest from Manchester City.
Any move would likely take place in August rather than July, with the former Santos star currently involved in the Club World Cup.
He started in Madrid's 1-1 draw against Al-Hilal in their tournament opener - providing an assist for Gonzalo Garcia's strike.
But he was benched during their 3-1 victory over Mexican side Pachuca, in Alonso's first win in charge.
Fabrizio Romano previously reported Arsenal ‘love’ Rodrygo but will not be in a position to bid for him until he informs Real of his desire to leave.
A lack of firepower in attack, namely at centre forward, derailed Arsenal's title bid last season, with Kai Havertz the club's highest scorer in the Premier League with just nine goals.
Arsenal are desperate to bolster their attack after limited options derailed their title charge
The Brazilian is said to be considering other options than Arsenal after interest from Man City
Mikel Arteta is also targeting Athletic Bilbao forward Nico Williams but their pursuit appears to be over with the 22-year-old set for a switch to Barcelona.
Meanwhile, they have also eyed Brentford’s Bryan Mbeumo but he looks destined to complete a move to Manchester United, who have submitted a second bid.
Chelsea's Noni Madueke has also been linked with a transfer to the Emirates.