Having failed to agree new contracts with their respective clubs, it has been well documented that the two players have been in a position to discuss transfers to foreign clubs since January.
Despite their situation off the pitch, the pair have remained important members of their respective squads, Christensen making 33 appearances and Kessie featuring in 38 games.
However, according to transfer expert Fabrizio Romano, the pair are all but confirmed as Barcelona players ahead of the 2022-23 campaign.
Romano says that their deals were signed weeks ago, with it appearing that their departures will not be confirmed until they have played their final games of the season next weekend.
Furthermore, Miguel Delaney of The Independent quotes Chelsea head coach Thomas Tuchel as saying: "We are losing, of course, Toni [Antonio Rudiger], we're losing Andreas. So this is tough and we already have gap close."
Christensen is said to have withdrawn from the FA Cup final on the day of the game after feeling unwell earlier in the week.