The Mirror says Defoe thrived under Harry Redknapp on the south coast after both Martin Jol and Juande Ramos failed to fully appreciate his talents at Tottenham.
It is understood that Defoe was last night considering his future after being made aware Redknapp is keen to work with him again.
Defoe was back in London yesterday after the Pompey players were given a day off.
After leaving the capital to join Redknapp, Defoe struck 10 goals last season to earn himself a call-up to the England squad which tackled the USA then Trinidad and Tobago.
This term he has already smashed in eight in all competitions, and Spurs fans chanted for his return on Sunday - despite goals from Darren Bent and new boy Roman Pavlyuchenko in the 2-0 win over Bolton.