The 27-year-old has fallen down the pecking order under Frank Lampard at Stamford Bridge and has not featured in any of their first three games this season.
Andreas Christensen and Kurt Zouma have started both Premier League games at centre-back, while Fikayo Tomori and Thiago Silva started the Carabao Cup win over Barnsley on Wednesday night.
This leaves Rudiger as fifth choice in the centre of defence and Lampard is happy to let him leave before the transfer window closes on 5 October, as a result.
German publication Kicker reports that Barcelona are keen on the defender and are in a strong position to sign him as new manager Ronald Koeman builds a new squad at the Camp Nou.
Roma, the club Chelsea signed Rudiger from, are also interested in doing a deal, with the Daily Mail report that Paris Saint-Germain want to agree a season long loan for the defender.
Asked about the situation with his central defenders on Tuesday, Lampard said: ‘With the centre halves I can’t have them all in the squad. I keep getting asked about the size of the squad.
‘There might be movement, we know that, but nothing is concrete so don’t read too much into those selections at the minute.
‘It will have to be things which are right for the club and individuals and me and in terms of what happens in the next couple of weeks.’