Manager Pep Guardiola, who turned to Mahrez after losing winger Leroy Sane to injury at the weekend, appeared to hint that he could return with a fresh bid at the end of the season.
"Maybe they didn't think it could happen but then he became available. We have to find solutions".
Dortmund says the teams have agreed on a transfer fee of 63.75 million euros ($80 million) - a record for the Premier League club.
Tottenham too are getting close to signing Brazilian Lucas Moura, who has fallen out of favour at French giants Paris Saint Germain with the arrivals of Neymar and Kylian Mbappe.
Swansea paid £18m to take forward Andre Ayew back from West Ham, 18 months after he left Wales for east London.
African superstar Pierre-Emerick Aubameyang, who has been in named in the CAF Team of the Year four times since 2013, has explained why he has joined Arsenal.
Watford's long-time servant Troy Deeney could fill the void and is valued at £16 million (RM88.3 million) to leave the club he has been with since 2010.
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Deputy Speaker Lechesa Tsenoli said given the R4.3 million budget set aside for SONA, they would not be entertaining these requests.
After an impressive run with the squad which included a 21-goal performance during the 2012-13 campaign, Aubameyang signed with Borussia Dortmund, putting together an impressive stretch which also included 25 and 39-goal seasons in addition to the 40 scores he accumulated previous year.
Instead, the 29-year-old committed his future by putting pen to paper on a three-and-a-half year contract extension.
However, a source said Ozil's decision was not related to the Aubameyang deal but that the German playmaker simply decided he wanted to remain at Arsenal and in London.
But Mourinho said: "Mata is very important".
"I spent five and a half wonderful years within the Arsenal family", he posted on Twitter.
"Now he's getting an extension of one more year".
Chelsea's proposed signing of Dzeko fell down partly on his demand for a contract until June 2020, a move that would have shattered the Blues' policy of not committing to players over the age of 30 for longer than a year.