Paris Saint-Germain winger Angel Di Maria is also said to be a target, with reports claiming the Argentine has asked coach Unai Emery to facilitate a move to Barcelona.
The 26-year-old left his global teammates earlier on Thursday "to formalise a transfer" with Barca one of a host of clubs linked to the Foxes star.
Mahrez left the Algerian national team camp on Wednesday night to complete his transfer away from Leicester City.
Arsenal have been strongly linked with Mahrez while Barca had considered him as a back-up option should they fail in their bid to land Philippe Coutinho from Liverpool.
Mattis On Trump's North Korea Tweet: 'We're Never Out Of Diplomatic' Options
Mattis may hope that Congress similarly steps in here to take this issue out of his hands-and to take on its political risks, too. Trump tweeted , a day after he said " All options are on the table " for dealing with Pyongyang.
The Algerian squad will therefore fly without him Thursday morning to Lusaka to face Zambia on Saturday.
Reports claim Mahrez has flown to Paris where he is now hanging out as he waits for a bid to be accepted by Leicester, but other reports claim he is in both London and Barcelona.
Mahrez had been linked with Roma in the early part of the summer window but that deal appeared to have gone dead.
Tottenham are desperately in need of a winger, and Riyad Mahrez given his experience in the Premier League seems to be the ideal signing for the North London club.
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