Puch, from Chile, went missing from an important training session on the eve of a match earlier this season and has spent most of his time since on the injury list.
Porta, who counts as Wasl's Asian player because of his dual Uruguay and Australia citizenship, has scored once in seven Pro League matches.
Marwan bin Bayat, the chairman of the club, confirmed in a television interview that Wasl are looking to replace Puch and Porta during the January transfer window.
He said the club are close to signing a foreign professional currently playing in the Saudi Arabia league, but declined to name the player.
Some media reports have suggested the player could be Argentine Juan Ignacio Mercier, who is playing for Al Nassr.
Maradona gave Mercier, a 31-year-old midfielder, his international debut in 2010 when Maradona was coach of the Argentina national team.
Mercier was an important member of the Argentinos Juniors team, who won the 2010 Clausura championship. He scored the opening goal in Argentinos' 2-1 win over Huracan in the final game of the season, which secured the championship.
In July, Mercier moved on a two-year deal to the Saudi club.
Some media reports have also linked Wasl with a move for the former Spain and Real Madrid star Raul Gonzalez, whose two-year contract with the German club, Schalke 04, expires at the end of the season.
The club have also identified Ferydoon Zandi, the Iranian-German professional, as a likely replacement for Porta to fill their Asian player slot.
Zandi, 32, an attacking midfielder, was part of the Germany Under-17 and Under-21 teams, and has 29 caps for Iran.
For the first nine years of his professional career, he played in the Bundesliga before moving to Cyprus. He is currently with Iran's Esteghlal.
Maradona has been asking for reinforcements over the last few months and warned of a cull following their 2-1 defeat at Al Wahda on Friday.
The Argentine described that performance in Abu Dhabi as Wasl's "worst" since he took over in June.
"There will be no place for any player who does not meet our aspiration," said Maradona, whose team have earned only two points in their last four games. "The team played really badly, and I did not expect this from them.
"We have become Santa Claus, distributing gifts in this Christmas period, and I hate that. I do not like giving gifts to my competitors. The team lacks personality, determination and the desire to win. I want us to win, but we keep making mistakes and that is unacceptable. I am really sad about that."