Chelsea have had a £13m bid knocked back by the Italian club, but the report claims the Stamford Bridge side can clinch an agreement if they improve their offer by £2m.
The Colombian international has been heavily linked with a move to Chelsea since November, with Jose Mourinho eager to strengthen his club's Premier League title push.
He all but ruled out the addition of another striker this month as he plans to go ahead with Fernando Torres, Samuel Eto'o and Demba Ba.
But with Michael Essien relegated to a bit-part role and Marco van Ginkel a long-term injury absentee, the Chelsea boss wants extra strength in depth in the central midfield position.
The report claims negotiations between Inter Milan and Chelsea are at an 'advanced stage' despite the £13m rejection.
Inter are holding out for £15m, a price they believe is Guarin's fair market value.
The Chelsea transfer target has appeared in all 17 of Inter's Serie A games this season, scoring three goals and providing four assists.