United are yet to decide who another transfer war chest will be handed to, with Carrick appointed on a short-term basis through to the end of the 2025-26 campaign. He has overseen four successive victories over Manchester City, Arsenal, Fulham and Tottenham.
Saha, who once played alongside Carrick at Old Trafford, believes his former team-mate should be considered for the top job on a permanent basis - even if the likes of Carlo Ancelotti and Zinedine Zidane are also in the mix.
Saha added: “I would love to see Michael given the chance. He's done very well. He's a very hardworking guy but humble as well. The results are going for him at the moment but not only the results, the way the team is playing and performing, we all can see the change straightaway. He's had the biggest impact since Sir Alex Ferguson.
“He does provide an answer to the question about the next manager. I do think they need to think about Carrick very, very, very seriously there.
“We know the expectation is so big and sometimes clubs have certain types of conversations and they want to see a long term plan. Do they see this is a spell where everything is going well for Carrick? Who knows how he reacts when he's under more pressure. So maybe he needs to be challenged in that sense to be considered for the full-time role. I don't know.
“What I see is that he understands the DNA of the club, he's been under pressure, maybe not as a manager but as a player, he understands how those managers have reacted before as he was part of the coaching staff. So he understands. He's not a rookie. So I do think he deserves his position but when names like Ancelotti, Zidane come into play, it's a kind of a different ball game.”