The Gunners are known to be in the market for defensive reinforcements ahead do the January transfer window, with Arsene Wenger desperate to bolster his rearguard and holding midfield areas.
Injuries to a host of players, including Jack Wilshere and Aaron Ramsey, have exposed a lack of depth in the middle, which Romulo is seen as the ideal man to address.
Romulo has been a target for the Londoners for some months, with reports from Russia having suggested that scouts from the club have been assessing his progress this season.
Their interest was thought to have cooled, yet now reports claim that an agreement could be sealed by the end of the week.
Arsenal are said to want the transfer completed as early as possible, with Wenger keen to get the enforcer to the Emirates Stadium soon.