Dubai businessman Al Fahim has yet to finalise his protracted takeover of Pompey, but he has lined up additions to Paul Hart's squad.
Pompey boss Hart is eager to improve his numbers before the close of the transfer window and could soon have Gutierrez and Zaki in his squad.
Zaki spent last season on loan at Wigan Athletic and has been offered the chance to return to the Premier League by Portsmouth, while Gutierrez could also secure a move to Fratton Park.
Gutierrez has been tipped to leave Newcastle following the club's relegation to the Championship and he was linked with a switch to Olympiakos earlier in the week.
Al Fahim has confirmed talks have been held with the Magpies over a deal for Gutierrez and he also hopes to tie up a swoop for Zaki.
"We are in negotiations with Amr Zaki to bring him in on a loan deal with a view to a permanent transfer," Al Fahim told Emirates Business 24/7.
"We are also speaking to Newcastle about the possibility of bringing Jonas Gutierrez to the club."