Ramsey will leave Arsenal at the end of the season when his contract expires and the Blues were one of a host of clubs monitoring his situation.
But the west London club have been left impressed with the homegrown midfielders at their disposal with Barkley and Loftus-Cheek pushing for regular minutes under boss Maurizio Sarri.
Sarri is not short of midfield options right now with Barkley and Loftus-Cheek battling with Jorginho, N'Golo Kante, Cesc Fabregas, Mateo Kovacic and Danny Drinkwater for starting berths.
Barkley has scored three times in his last three games and earned a recall to Gareth Southgate's England squad as he continues to impress under Sarri's guidance.
And Loftus-Cheek has four goals in his last three games as he pushes to establish himself in the midfield.
Kovacic is on loan at the club from Real Madrid and with no plans to make it permanent, plus the doubts over Fabregas' future, the club targeted Ramsey in a bid for reinforcements.