A bid could be around $3 billion, according to Russian business daily Vedomosti, which earlier reported the news, and would rival a bid from another privately owned investment group, Summa Group, the paper said.
"We can say only that A1 sent to VEB a request for loan to buy Domodedovo," a representative for A1 said in an email, referring to Russian state development bank VEB.
He declined to comment further.
A1 owns a diversified portfolio of investments ranging from retail and cinemas to steel and oil
Domodedovo's billionaire owner Dmitry Kamenshchik attempted to list the airport on the London stock market last May, but canceled the initial public offering two weeks later after failing to get the right price.
Valuations for the airport were put at between $3.5 billion and $7.5 billion by Goldman Sachs and $4.2 billion-$5.3 billion by Citi during the IPO attempt, sources told Reuters at the time.
Vedomosti reported on Tuesday, citing an unnamed source, that A1 and VEB aimed to bid jointly for the airport.
According to Vedomosti, A1 will offer around $3 billion for Domodedovo, the same as Summa, which had agreed financing with state-controlled lender Sberbank.
The deal would be subject to approval by Prime Minister and President-elect Vladimir Putin, Vedomosti said.
Summa is involved in projects ranging from oil to telecoms and has stakes in two grain export terminals in Russia's main deep sea port of Novorossiisk.
VEB declined to comment.