The Crystal Palace trio were due to leave on free transfers this summer.
Crystal Palace are close to agreeing new deals for three out of contract players, according to the Guardian.
And the report adds that Palace are also set to offer a new deal to Wilfried Zaha, which could see the winger's £110,000 weekly wage increased to above that of Christian Benteke - the club's highest earner.
There is no mention, however, of Martin Kelly, Damien Delaney, Chung-yong Lee and goalkeeping trio Wayne Hennessey, Julian Speroni and Diego Cavalieri, whose contracts are all due to expire next month.
Crystal Palace have already agreed to sign Getafe 'keeper Vicente Guaita, and are unlikely to pursue their interest in Alban Lafonte of Toulouse as they wait the Spaniard's arrival, according to the Guardian.
Midfielder Cabaye has been strongly linked with a return to France with Europa League runners-up Marseille.