The Sky Sports News reporter has claimed that the trio are among the players Chelsea are keeping tabs on as they look to further strengthen their squad this summer.
Chelsea have been relatively active in the summer transfer window so far, having concluded deals to sign Willy Caballero, Antonio Rudiger, Tiemoue Bakayoko and Alvaro Morata.
However, the Blues also lost Nemanja Matic on Monday after the Serbia international completed a £40m move to Manchester United.
The west London side are thought to be on the lookout for further reinforcements in midfield ahead of next season, and Gilmour claims that the Premier League trio are among their targets.
Speaking on Sky Sports News on Tuesday morning, Gilmour said: “Chelsea’s other midfield targets [after Drinkwater] include Everton’s Ross Barkley and Arsenal’s Alex Oxlade-Chamberlain.”
Chelsea are now preparing for their Community Shield showdown with Arsenal at Wembley on Sunday afternoon as they look to begin the season by winning a trophy.
Arsenal beat the Blues 2-1 in the FA Cup final at Wembley back in May.
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