The Daily Telegraph says the Blues are keen to bring in additional full-backs to provide competition to Victor Moses and Marcos Alonso, with Cedric. Juventus defender Alex Sandro and Paris Saint-Germain right-back Serge Aurier are among the names under consideration.
Chelsea had a £52m ($67m) bid rejected for Sandro earlier this summer and made fresh enquiries about the left-back this week, but were rebuffed by Juventus.
Cedric has three years left on his contract at Southampton but he would be cheaper compared to other options, with Chelsea hopeful of having a bid of around £20m accepted for the Portugal international.
Blues boss Antonio Conte has persistently complained over the size of his squad, even though the likes of Alvaro Morata, Antonio Rudiger and Tiemoue Bakayoko have been brought in to Stamford Bridge over the summer.
The defending Premier League champions have sold, released or sent out on loan a total of 32 players this transfer window, leaving Conte concerned over the depth of his squad.
"I hope to be able to improve our squad. The transfer market is not finished. We want to be competitive and we want to fight for the title again. The club knows my priorities," Conte told Sky Sports earlier this month.
"It's a great challenge for us to try and retain the title, but we are working hard."
The former Italy boss went on to describe Nemanja Matic's departure to Manchester United as a "great loss".
Chelsea stumbled to a 3-2 home defeat against Burnley on 12 August – the first time the Blues have suffered a defeat on the opening day of the season since 1998.