Commercial director Dmitry Denisov, the company's acting president, is considered the main contender for the post.
Chuikin said he was leaving the company after his contract expired last month, RBK Daily reported.
Chuikin was appointed Yevroset president in June 2007, his appointment coinciding with the announcement by the company that it was planning an initial public offering in 2008.
Chuikin was plucked from Dixis, a smaller competitor, where he was general director, to replace Eldar Razroyev, who left Yevroset after three years as company president.
Chuikin said earlier this year that Yevroset could sell as much as 25 percent of the company in a share flotation to help restructure about $840 million of debt.
"We had several interesting offers from various financial institutions," Chuikin said in January. "But there aren't any active ongoing negotiations."
A failure to deliver on the IPO could be one reason why his tenure was so brief, industry experts said.
"Chuikin's speedy exit may be connected with lack of progress with the IPO flotation planned for this year," said a telecoms industry source, who requested anonymity as he was not authorized to comment on restructuring issues.
"This is [most likely] because it often takes more than a year before a chief executive gets results," the source said, adding that a one-year contract for senior executives was not uncommon with mobile phone retailers such as Yevroset.
Another industry source, who requested anonymity because of the sensitivity of the issue, said Yevroset's strategy of offering many of its phones at discount prices needed reviewing. The departure of several senior Yevroset managers in recent months, including Andrei Rukavishnikov, vice president for marketing, could be traced to the lack of a new strategy, the second source said.
Yevroset is co-owned by board chairman Yevgeny Chichvarkin and Timur Artemyev, another director.
The company sold 12.6 million mobile phones in 2007, up 4.2 percent compared with the previous year.
Gross sales jumped 21 percent to $5.61 billion in 2007, pushed up by more-expensive handsets while its market share reached 35 percent.
The company said it expects sales revenues to grow by 6 percent to 8 percent in 2008.
Yevroset currently operated 5,146 outlets in 11 former Soviet countries.
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