The company's Toronto-listed stock rose as much as 18.27 percent in morning trading to C$21.69, but was still below the offer price of C$24 per share.
The offer represents a premium of 30.9 percent to Amaya's Friday close.
Amaya, which also reported better-than-expected results on Monday, said it would consider Baazov's offer.
Baazov, who already owns about 17.2 percent of Amaya, including options, said he made the offer on behalf of a to-be-formed entity led by him.
The offer including debt and transaction costs is valued at $6.7 billion, Amaya said in a regulatory filing. (http://bit.ly/2fNeaSG)
The equity portion of the deal would be $4.1 billion and will be mostly financed by four funds, which have committed $3.65 billion and Baazov's shares.
"I think a lot of groups would like to have this business," Macquarie research analyst Chad Beynon said, adding that Baazov was placing a higher valuation on the company than the industry.
Baazov said that the to-be-formed entity will pay $200 million of the $400 million deferred purchase price Amaya had to pay for its acquisition of Rational Group. He added the entity will release funds in advance, if the payment is due before the deal closes.
Amaya, which owns gambling websites PokerStars and Full Tilt, said in February it had received a non-binding proposal from Baazov to take the company private for C$21 per share.
Two months after Baazov made the offer, he was charged with insider trading by Quebec's securities regulator, and the company said he was taking an indefinite paid leave of absence.
The charges followed an investigation into Baazov and other executives in 2014 for trading in Amaya's stock ahead of the company's $4.9 billion takeover of PokerStars-owner Rational Group.
British bookmaker William Hill Plc and Amaya abandoned merger talks in October, after the deal was thrown into doubt when a leading investor in William Hill said it would oppose the plan.
On an adjusted basis, Amaya earned 42 cents per share in the third quarter ended Sept. 30, beating the average analysts' estimate of 38 cents, according to Thomson Reuters I/B/E/S.
Amaya's total revenue rose 9.5 percent to $270.8 million from $247.3 million, marginally higher than the average analyst estimate of $270.1 million.
(Reporting by Arathy S Nair and Vishaka George in Bengaluru; Editing by Martina D'Couto)
