After the Eagles secured their status in the top flight for another 12 months with a 4-0 win over Hull City, Allardyce can now plan what business he would like to conduct ahead of the next campaign.
According to The Sun, both of the Manchester City defenders have been identified as targets after it emerged that they are both likely to leave the Etihad Stadium at the end of the season.
Their respective contracts expire next month and with Pep Guardiola promising a shake-up of his squad, it appears that no effort will be made to keep them at the club.
With the new Premier League television deal now in full force, Palace are likely to be able to meet their wage demands as they look to strengthen their backline.
They are well stocked at full-back, but any outgoings would help push through moves for both of the French internationals.