Ziyech and Kovacic were both doubtful for the Wembley showpiece after picking up injuries in Chelsea's routine 2-0 UEFA Champions League win over Lille in midweek, while James has not appeared since 30 December (AEDT).
Chelsea is seeking its fourth trophy under Tuchel, having already won the UEFA Champions League last season, the UEFA Super Cup, and the FIFA Club World Cup.
The Blues will also be the first team in English football history to compete in one of the major domestic cup finals (League Cup/FA Cup) in six consecutive campaigns on Monday (AEDT), having reached FA Cup finals in 2017, 2018, 2020 and 2021, and Carabao Cup finals in 2019 and 2022.
The Chelsea head coach's cause has been aided by the return of several key figures ahead of the clash with Jurgen Klopp's side.
"We had training today with everybody out on the pitch, except for Ben Chilwell," Tuchel said at the pre-match press conference. "It's brilliant news.
"Both [Ziyech and Kovacic] are okay, today they were not out training with separate programmes, everybody joined in with team training.
"We have no [bad] reactions, only positive reactions. I hope it will stay like this. We have another training session tomorrow, but we hope to have everybody available."
James recorded four goals and five assists in the first half of the Premier League season, and could provide another boost for Tuchel, who remains excited by the prospect of the wing-back's return.
However, the German boss conceded that he was unsure whether James would be fit enough to start at Wembley.
"He looked brilliant in the last two training sessions," the German added. "Let's wait another session and let's see if I'm crazy enough to put him on the pitch."
Tuchel was guarded as to which of his goalkeepers would start against the Reds, with Kepa Arrizabalaga starting all five matches in the competition so far, while Edouard Mendy has starred in trophy wins for both club and country in 2022.
Asked about the goalkeeper decision, Tuchel responded: "I will not tell you. I will take the decision later.
"Kepa played in the [FIFA] Club World Cup semi-final and brought us to the final, but then we took the decision to go with Edou for the final, who was back from the Africa Cup of Nations.
"The last decision will be taken after training, as always. Kepa did fantastic in the period that we had to be without Edou, so it's [both] an uncomfortable and very comfortable situation to be in."
Kepa refused to be substituted as Chelsea was beaten in its previous Carabao Cup final appearance, losing on penalties to Manchester City in 2019 under Maurizio Sarri.
But the goalkeeper has impressed with two clean sheets in four league appearances during Mendy's recent stint on international duty, leaving Tuchel with options heading into the domestic final.