Pompey finished eighth in League One in the recently-concluded season and John Mousinho is looking to build on a solid campaign by making a host of signings across the pitch.
The Portsmouth boss wants to bring in reinforcements with a view to challenging for promotion to the Championship in what is sure to once again be a competitive League One.
The club are looking at several players who will be available on a free transfer this summer and Chislett is one of them.
It has been claimed that they have considered the midfielder as an option but for now, Portsmouth are unlikely to try and sign him.
The 24-year-old South African has scored eleven times in 51 appearances across all competitions for Wimbledon this season.
He will be out of contract at the end of this month and several clubs are looking at him as an option.
Portsmouth have also been keeping tabs on him but it seems unlikely that he will end up at Fratton Park next season at present.
