The announcement comes ahead of a mid-November deadline for Russian billionaire Mikhail Fridman and Turkcell's founder Mehmet Emin Karamehmet to resolve a dispute over control of the Turkish company.
Alfa, part of Fridman's business empire, has been locked in a tussle over Turkcell that stretches back almost a decade with equity partner Cukurova, which is run by Karamehmet.
In July, a London tribunal dismissed claims against Fridman and required Cukurova to choose within 60 days either to buy Fridman's shares in Turkcell for $2.7 billion or sell its own stake to Fridman for $2.8 billion.
In September, the tribunal pushed backed the deadline to 60 days from Sept. 19.
Fridman indirectly holds 13.2 percent of Turkcell while Karamehmet indirectly holds 13.8 percent. Swedish phone carrier Telia Company (TELIA.ST) owns 37 percent.
VTB said in a statement the agreement reflected the intention of VTB and Alfa to invest in Turkcell "in relation to the possible increase of Alfa Group's stake in the operator".
VTB's press service declined to elaborate on the financial terms of any possible investment.
The bank said in its statement such a deal would reflect its desire to diversify its investment and loan portfolios.
Fridman's investment vehicle LetterOne did not immediately comment on VTB's announcement.
Cukurova could not immediately be reached for comment.
Reporting by Alexander Winning and Anastasia Teterevleva; editing by David Clarke