Tuchel remains backed by the FA criticism aimed at his late substitutions after the Three Lions surrendered a lead.
The German coach has confirmed his intention to stay and guide England towards Euro 2028.
However, former England captain Rooney believes Guardiola would be the ideal alternative if the ex-Manchester City boss becomes available.
"I don't see anyone else out there at the minute, unless you go and get Pep Guardiola. If Pep is available, then maybe you go and get him," Rooney said on The Wayne Rooney Show.
"I think he is a top-class manager and what the top managers do, they learn from the mistakes and they improve and get better.
"If we sack him, what managers are we going to bring in? And I don't think there's anyone out there who's as good as Thomas Tuchel, unless Guardiola.
"But the big thing for me is he's not experienced at World Cups. We had the exact same with (Fabio) Capello.
"The World Cup is different and you need to feel that environment and now he's felt it."