Lucas Silva, 21, had been strongly linked with a move to the Bernabeu, the player himself had been talking about a potential link-up with Cristiano Ronaldo.
However Madrid have so far refused to improve on their opening offer of 12 million euros.
However, Arsenal are believed to have lodged a bid of 15 million euros, meeting Cruzeiro's asking price and look set to tie up the transfer.
However Gunners could face stiff competition from Manchester United who are determined to strengthen their squad in the pursuit to finish in the top 4.
Silva has been earning rave reviews in his home country, and has been compared to Yaya Toure already.
With Arteta Injured, Arsenal are in dire need of a DM, Silva could very well be the solution to the Gunners defensive problems.