Both have been touted to have bright futures, with Danish youth international Christensen featuring in two post-season friendlies against Manchester City in 2013.
While a deal for Zouma is more likely, with head coach Jose Mourinho keen on using experience in the first-team next season, the Daily Mail is reporting that Sunderland are also interested in acquiring Christensen and Baker.
It seems that a deal for Christensen would only go through if Zouma stayed at Chelsea, although both could fit into the same team, with the Dane able to occupy a position along the entire defensive line, as well as a deep-lying midfield role.
Baker, who made his first team debut for the Blues in an FA Cup match in January, has been compared to Chelsea and England legend Frank Lampard, with his technical ability and goal-scoring record - better than one-in-two for England Under-19's - being praised from all corners of the media.
He would add a further attacking option to the Sunderland midfield, with his directness and eye for goal different from the current first-team squad - which is comprised of both defensive-minded and fleet-footed midfielders, but no overt goalscorers.
Both players would reportedly be arriving on temporary deals, with a full-season loan said to be the favoured move for both clubs. Chelsea have no intention of losing their starlets permanently, securing their futures to Stamford Bridge with contracts rewarded in 2013.
Sunderland may be hoping that sporting director Lee Congerton can influence any potential deals in his favour, with a host of contacts at Stamford Bridge following a spell with the West London club.
Having originally been appointed youth coach in 2005 by Mourinho, the Welshman became chief scout following the the arrival of Frank Arnesen. Alongside then-reserve-team coach, and current Liverpool manager, Brendan Rodgers, Congerton oversaw the arrival and integration into the first-team of a selection of highly rated prospects, including Ryan Bertrand and Daniel Sturridge.
Since arriving on Wearside in March 2014, Congerton has agreed deals with Costel Pantilimon, Billy Jones and Jordi Gomez to arrive on free transfers, and has overseen the contract extension recently signed by winger Sebastian Larsson.
It promises to be a bright campaign for Sunderland, as they attempt to carry their late season form into August. With a selection of well thought out signings, and the potential arrival of Chelsea's highest rated youth prospects, the Black Cats could be looking towards a top-half finish - and even a Europa League spot.