The 23-year-old midfielder has found first-team opportunities limited since arriving in west London in the summer, from Werder Bremen for an undisclosed fee.
The German international has made just four Premier League appearances so far in 2012/13, with three of those coming from the Chelsea bench.
Marin has featured more regularly under the interim management of Blues boss Rafa Benitez, with cameos coming in the League Cup, FA Cup and Club World Cup competitions.
However, Marin's infrequent playing time means that he could be open to a short-term switch away from Stamford Bridge, as he looks to establish himself on the international scene.
"I must admit that Marin has some interesting proposals to go on loan until the end of the season", his agent, Fali Radamani, told Izvestia.
"I cannot name the clubs, but I can say that proposals came from both Western Europe and Eastern Europe.
"Marko wants to get more match practice, but we understand that at a super club like Chelsea there will always be serious opposition."
Radamani was quick to point out that his client has no regrets over his decision to join Chelsea, but added that it may be beneficial for both parties that he be allowed to leave this month.
CSKA Moscow are reportedly eager to secure Marin's signature, and have even sent their loan proposal directly to Chelsea owner Roman Abramovich.
"Marin feels fine in London, but to consistently be called up to the German national team, you must be a player in the starting line-up," added the player's representative.
"In the near future we will discuss with the leaders of the club all the best possible options for the player's career."