Pompey boss Paul Hart reportedly sees the player, who was apparently offered trials by a clutch of Premier League clubs, including Sunderland, Stoke City and Wolverhampton Wanderers, as a replacement for Glen Johnson, who moved to Finnan's former club Liverpool earlier in the summer.
"Steve Finnan is one of many people we are interested in," Hart told BBC Sport earlier.
"Steve is a quality player and if you saw my list you could probably see a few more quality players there."
Finnan has left Espanyol only a year after joining them from Liverpool, as he endured a frustrating time in Catalunya, where injury limited his capacity to impress, with the 33-year-old being linked with possible January moves to Hull City and Tottenham Hotspur.
However, he opted to stay in the winter, but it looks now as though his sojourn in Spain is over, as Sky is reporting that the player's agent has informed them he has completed a medical on the South Coast.
Zack Wilson, Goal.com