It is understood a deal with the centre-back could be sealed as soon as today.
He’s been on the south coast finalising his switch.
Downing will arrive as a free agent following his release from Blackburn Rovers.
League One rivals Doncaster were highly keen to land the 27-year-old on a permanent basis after he spent the second half of last season on loan at the Keepmoat Stadium.
But the Blues are set to win the race.
Pompey boss Kenny Jackett has been a long-time admirer of Downing, having had him on his radar during the January transfer window.
The former West Brom and Walsall defender made 22 appearances during the second half of last season at Donny, featuring in both legs of the play-off semi-final defeat to Charlton.