The Blues have opened talks with the out-of-contract defender, who has proven such a pivotal figure this season.
Burgess has made 208 appearances and scored 12 times since joining Pompey in the summer of 2015 under Paul Cook.
However, his existing deal expires on June 30, which would render him a free agent this summer.
Earlier this month, Kenny Jackett spoke of his desire to retain the 28-year-old after the club relaxed their policy of not holding contract negotiations.
The Blues’ chief executive, though, insists agreement has yet to be reached.
Catlin said: ‘Christian is our player, we speak to him every day, whether it be me or Kenny, it’s not like we are not speaking.
‘But at this moment in time we haven’t reached any agreement for him to sign next year and he continues to be contracted until June 30.
‘We haven’t reached any agreement on a new deal.
‘We are talking to him every day in one scenario or another, but, at this moment, the priority is really to complete this season and try to get promoted.’
Burgess is among 12 members of Pompey’s first-team squad out of contract at the season’s end.
They include loanees Sean Raggett, Ross McCrorie, Steve Seddon and Cameron McGeehan, who are scheduled to return to their parent clubs.
The others are Brett Pitman, Oli Hawkins, Lee Brown, Brandon Haunstrup, Luke McGee, Adam May and Matt Casey.
Burgess has made 42 appearances this season, recently serving a two-match suspension, a spell during which the Blues collected one point from a possible six.
Undoubtedly he will be in the running for player of the season honours, following a string of consistently-high performances this term.
In addition, the centre-half has scored four goals since the turn of the year to help drive the Blues into fourth place in League One.
During Burgess’ time at Fratton Park, he has won the League Two title, the Checktrade Trophy, reached two play-off semi-finals and also has a Leasing.com Trophy final on the horizon.