Van Gaal's men take on Les Lions de la Teranga on Monday, 21 November, looking to start their FIFA World Cup campaign off with a win.
Mane, 30, will not be part of that match nor the tournament as a whole after he suffered a leg injury while playing for Bayern Munich earlier this month.
The Senegalese was selected in Aliou Cisse's 26-man squad but withdrew due to the injury.
Van Gaal has showered praise on the former Anfield attacker and compared him to Barcelona forward Memphis Depay.
He also revealed how he tried signing him while manager of Manchester United, saying (via vi.nl):
"Senegal will miss Mane very much, but for us it is a loss that Memphis does not start. We miss our top scorer and assist king. Mane is a special footballer, I wanted him too when I was manager of Manchester United. I'm a fan of his."
Mane was in form heading into the FIFA World Cup in Qatar, scoring 11 goals and providing four assists in 23 appearances across competitions.
He has long been Senegal's protagonist, helping the nation win the Africa Cup of Nations in February of this year.
The ex-Liverpool winger scored the decisive penalty in a 4-2 penalty shootout victory.
Mane has earned 92 international caps for Senegal, scoring 33 goals and contributing 20 assists.
Manchester United legend Wayne Rooney is excited to watch Liverpool's Trent Alexander-Arnold at the FIFA World Cup
Alexander-Arnold has had a difficult spell at Liverpool this season, with many questioning his defensive capabilities.
The 24-year-old right-back has made 20 appearances, scoring three goals and helping the Reds keep seven clean sheets.
When the Liverpool defender was named in Gareth Southgate's squad, some argued that he wouldn't be heading to Qatar if Chelsea's Reece James wasn't injured.
However, Rooney looks forward to seeing how the Reds right-back fares at the World Cup.
The Manchester United hero was quoted as saying (via Liverpool Echo):
"I’m really intrigued to see what Gareth Southgate does with Trent Alexander-Arnold. Personally, I would start him."
Alexander-Arnold missed England's last major international tournament when he suffered a thigh injury just days before the European Championships began in 2021.
He has earned 17 international caps for the Three Lions, scoring one goal and providing four assists.