Podolski completed his first training session in Milan on Monday, thrashing a shot into the top corner during a practice match in a decent showing from the German.
The 29-year-old spent the weekend in Milan but could not train with his new team-mates due to delays with the necessary paperwork.
Mancini named his 25-man squad after training for Inter's trip to Juventus on Tuesday and Podolski made the cut, although the coach insisted his new acquisition will not start, declaring "he'll definitely sit on the bench".
The former Manchester City and Galatasaray boss wants to do more business in January, claiming he needs another winger to complement Podolski.
Inter have been linked with Bayern Munich's Xherdan Shaqiri, Ezequiel Lavezzi of Paris Saint-Germain and Hajduk Split youngster Tino-Sven Susic, and although Mancini seemed interested with all three on Monday.
"We needed two wide players and Podolski is one of them. He's 29 years old and has a wealth of experience so I hope he can make a telling contribution to the team," the 50-year-old said.
"Shaqiri is another who could do a job for us but he's a Bayern Munich player. He's a young guy so it's an interesting one for the future, too.
"Lavezzi? Look, he's a PSG player and I think that's a difficult one for us. I don't know what's going to happen, so let's see. Susic is a young player with great quality – he has a big future ahead of him."
Inter currently languish 11th in the Serie A standings, with a solitary league win since Mancini returned for a second spell at the helm in November.
Mancini's men face a tough test in their first league fixture since the winter break with Serie A leaders Juventus awaiting them in the Derby d'Italia.
But Mancini wants his team to believe in themselves and not go into the match taking too much notice of the 18-point gap between them and Juventus.
"We're Inter – we're a big club – and we play every match to win. We might not always end up on the winning side but it's important to have a certain mentality," Mancini said.
"Getting a result in such a big match would give the team a massive boost.
"When the time comes tomorrow, I don't want to see a team that goes out onto the pitch thinking it's an impossible task. I don't think there is the distance between Juventus and Inter that the league standings of the last few years would seem to indicate."
