The club, thought to be Anzhi Makhachkala, then offered a blockbusting £460,000-a-week (Sh63.204m!) deal to the Argentine superstar, a massive £24m (Sh3.27b!) a year after tax.
Barcelona were obliged to accept the massive offer but a gob smacked Messi quickly rejected the move after discussions with Barca president Sandro Rosell and his family.
The three-time World Player of the Year, who scored a record breaking 91 goals this calendar year, then pledged his future by signing a new deal with the Catalan giants.
The approach came during negotiations that ended earlier this month with the Argentinian signing a two-year contract extension at the Nou Camp.
While the story in El Mundo Deportivo, a Spanish sports daily, does not name the Russian club, billionaire-owned Anzhi are felt to be the likeliest candidates.
Anzhi made ex-Barca striker Samuel Eto’o the game’s highest paid player when they signed him last year.
Messi, 25, has won the Ballon d’Or, awarded annually to the world’s best player for two years in a row and is widely tipped to make it three on the spin.
He also set a football record that may never be broken in 2012, scoring 91 times for club and country in the calendar year.
The previous best, set in 1972 by West Germany striker Gerd Muller, was 85.