Blues boss Maurizio Sarri has found it difficult to placate Christensen's desire for first-team football this season, having not used him once in the Premier League.
However, Christensen will not be on the market and Sarri has instructed the 22-year-old to remain patient, with Antonio Rudiger and David Luiz being Chelsea's current first-choice centre-backs.
Chelsea are more open to allowing Gary Cahill to leave with only seven months remaining on his current contract.
Cahill has enjoyed a glorious seven-year spell at the club, winning every major honour, but the 32-year-old has also expressed his frustration at a lack of regular minutes this term.
After playing 40 games under Antonio Conte last season, Christensen has faced repeated questions about his future at Stamford Bridge.
When asked if he would leave in January, Christensen told Sky Sports earlier this month: "Difficult question. No, I don't think so.
"Things are different from last season. I played a lot of games [last season] but this season it hasn't been like that. It's always difficult for a player but we'll see what happens."
Sarri would ideally like to keep Christensen and Cahill in January, after giving the club captaincy to the latter, and instead allow Ethan Ampadu, 18, to depart on loan.
Ampadu recently renewed his contract but has had little game time as Chelsea's fifth-choice centre-back and he has interest from Championship duo Derby County and Aston Villa.
Chelsea are also keen to renew both Rudiger and Luiz's contracts, as well as star men Eden Hazard and N'Golo Kante.