The 35-year-old became a free agent in December when Besiktas mutually agreed to terminate his contract and he had been expected to return to his homeland with Porto.
However, LEquipe report that Pepe will join the clutch of experienced campaigners Henry is trying to draft in to save Monaco from relegation, along with Cesc Fabregas and Naldo.
Arsenal are also in the market for a centre-back, and the report claims the Gunners made a late approach for Pepe but were rejected.
Unai Emery has made little secret of his desire to bolster his options at the back, particularly after Rob Holding suffered a season-ending injury.
Speaking after beating Blackpool in the FA Cup, Emery said: Maybe the transfer market can help us with a centre-back, but it is not easy because also [Konstantinos] Mavropanos is also coming back after injury.
Another name in the mix to join Arsenal is Juventus centre-back Medhi Benatia and there have even been suggestions the Moroccan could be included in a swap deal for Aaron Ramsey.
Monaco, meanwhile, are hoping to wrap up Fabregas move to the south of France as early as Sunday evening, with both the player and his agent, Darren Dein, travelling to the principality for a meeting with club president Vadim Vasilyev.
The French side have already signed Naldo and want to partner him with Pepe, though he could yet snub Monaco at the eleventh hour and return to Portugal at the request of his family.
More: Arsenal FC