Mundo Deportivo claims that the player's agent, Rene Ramos, has been approached by the trio after the 22-year-old forward made an impressive debut with the Barcelona first-team during the Catalan's 3-0 victory at Murcia in the first leg of the Copa del Rey last-32 on Tuesday night (24 October).
Arnaiz scored the third goal at Murcia and manager Ernesto Valverde suggested after the game that his promising debut will only be the "first step" on his way to the first-team.
"He has grown as the game progresses. He was a little more misplaced at the start but in the second half he has participated much more. He has the goal in his head and has a powerful shot. He has scored a great goal. I think he can help us," Valverde said.
"He is already helping Barcelona B but we are not two teams. We are just one: We are Barcelona and we hope this first step that he has taken can help us in the future."
Mundo Deportivo says that the Barcelona boss was not the only one impressed with Arnaiz's debut though.
United, Arsenal and Bayern were also alerted by his eye-catching performance at the Nueva Condomina with the Spanish publication claiming that representatives from three European giants quickly called Arnaiz's agent after the game to enquire about his contract situation at Barcelona.
Mundo Deportivo says that both United and Arsenal "like Arnaiz" a lot because they believe that his pace and ability to beat a player will be a perfect fit for the Premier League.
Meanwhile, Bayern see the skilful winger as a potential long-term replacement for 34-year-old Franck Ribery.
The Spanish publication adds however that Arnaiz is determined to make a breakthrough at the Nou Camp after having turned down the likes of Real Madrid and Juventus to join the Catalans' second team in the summer.
Arnaiz proved himself in the Spanish second division with Valladolid last season after scoring 12 goals in 35 appearances.
In the summer Real were said to have the advantage in the race to secure his services with the brother of captain Sergio Ramos', Rene Ramos, representing Arnaiz.
However, Barcelona eventually won the race in a €3.4m (£3m) deal which could increase to €8m if certain add-ons are met.
Mundo Deportivo understand that Arnaiz is now only thinking of making the next step to Valverde's side following an impressive start to the life with the Catalans' second team, having netted four goals and provided three assists in first his nine games at the club.
However, United, Arsenal and Bayern may still be tempted to make a move to lure him away from the La Liga giants with his current release clause set at only €20m (£17.9m).
On 28 August, following his arrival from Valladolid, Barcelona said that Arnaiz had agreed a three-year contract with an option for another two, with his release clause set to increase from €20m to €40m once he signs the extension.