Neymar spent four trophy-laden seasons at Camp Nou before joining the French giants for a record €222 million (£200m/$262m) in August 2017.
He has since been embroiled in a court battle with his former club over an alleged breach of contract and unpaid loyalty payments.
Amid fresh rumours last week linking Neymar with a return to Catalunya, Font has ruled out making an approach for the 28-year-old.
"Institutionally, Neymar's not in my plans," said Font, who has previously stated he wants to bring Pep Guardiola back to the club to reunite the Catalan coach with Lionel Messi.
"For financial reasons and for other reasons, like the lawsuit he has against the club and the fact he left the club in a tricky position days before the season started [in 2017]."
Neymar has scored 49 times in 56 Ligue 1 outings since arriving at PSG and assisted a further 29 - only team-mate Kylian Mbappe (95) has been directly involved in more goals in the competition in that time.
During his time with Barca, meanwhile, he was directly involved in 164 goals in 186 appearances, helping the club to eight trophies.
"He would fit in on the sporting side but not on the financial or the institutional side of things," Font added in the interview with Sport.
"But the signings will be in the hands of the sporting directorate, not as they have been made up until now."
Barcelona have been without an official president since Josep Maria Bartomeu resigned at the end of October ahead of an expected vote of no confidence.
Font is the heavy favourite to win the election, which is scheduled to take place on January 24.
He may have a number of issues to address if he is to take control of power at Camp Nou, with it possible that Messi – who is only tied to a contract through to the summer of 2021 – will have spoken with suitors outside of La Liga by the time Barca get their new president in place.