The Algerian was desperate to leave Leicester City in the summer, having left his national team duties to force through a move on deadline day.
One of the interested parties were the Gunners, but Leicester's unwillingness to negotiate anything less than their £44million valuation killed the deal off.
The 26-year-old has since returned to flying form after a slow start to the season. In his last seven matches, Mahrez has scored four goals and played an integral role in the return of the Foxes to the top half of the Premier League table.
It is reported that they're prepared to fork out £26million for the 2015/16 PFA Player of the Year.
However, the saga is expected to drag on throughout the entire transfer window, with an agreement due to conclude towards the end of the month.