The Gunners retain an interest in the France international, but a move seems unlikely given the prices being quoted.
The 22-year-old has enjoyed a stellar campaign in Ligue 1 this season, and was a star performer in Monaco's Champions League run, with a particularly fine performance put in against the Gunners as Arsene Wenger's men were sent packing at the last-16 stage.
The France international only joined Monaco from Sevilla two years ago but has impressed ever since - with Arsenal manager Arsene Wenger said to have followed him throughout his time at Lens and with the Spanish side, remaining keen on him at all times.
His current employers have reportedly slapped a £25million price tag on their star man to ward off interest, with Inter Milan the first side to have made an enquiry about his services.
Whether a deal could be struck is another matter entirely, with Wenger having recently told Sky Sports that he does not expect big-money arrivals at the Emirates this summer, which a move for Kondogbia would certainly constitute.
It would also be interesting to see where any potential move would leave youngster Francis Coquelin, who has impressed since breaking through earlier in the season, with his performances having all but removed the need to sign a defensive midfielder.