Tottenham kick-started life under new head coach Frank with a 3-0 home success over Burnley and will hope to continue their form against City, who picked apart Wolves 4-0 in their first fixture.
They looked set to have Eberechi Eze available for the match, but the Crystal Palace star is now heading to their rivals following a late approach from Arsenal.
Eze snub
"You know of course I don't speak about specific players unless they are at our fantastic club," Frank told reporters ahead of Tottenham's trip to Manchester.
"To be very, very clear, I don't want any players who don't want to come to the club.
"If they don't want to come here and wear this fantastic badge, we don't want them here. That's very clear, and I imagine the fans feel exactly the same. That's a key message."
Team news
Frank also gave some team news and confirmed that two players will miss the clash.
"Destiny (Udogie) is better, trained with the team twice, full training, just too soon to be involved for City. We want him to train tomorrow and have another good week next week. He looks in a good place, very positive about him.
"(Ybes) Biss will miss this game as well. (Dejan) Kulusevski is out, that’s a longer one, I don’t want to put a timeline on it."
Further signings planned
Questions then moved to potential incomings, and although he did remain tight-lipped, Frank confirmed that the club are working hard to bring in new additions.
"We are in the market and we will look to strengthen the team. We have a good squad and good players. I see 23 players working hard on a game plan for Manchester City tomorrow.
"We need to do everything we can to be as competitive as possible. I am confident we will sign a player before the end of the window.
"(We currently have) two players in, two players out, so probably a bit similar. It’s the same level but that’s good. It’s my job and that of my staff to make sure we can compete.
"Every club wants to sign players as early as possible, but it's not that easy. I'm a positive guy, I'm not that fearful. I believe something will happen."
"It’s a couple of things, the club is working very hard to see if we can strengthen the squad with players who can improve the squad. That’s what we’ll continue doing until the end of the window."
Richarlison essential
Finally, Frank opened up on his attacking options and revealed that Richarlison is crucial to his plans going forward after two stunning goals against Burnley.
"Right now, he is my starting nine. He scored two fantastic goals. He had two top games.
"He’s a very good player, I’m very happy with him. Richy wants to stay, I want to keep him. There have been no talks about anything else.
"We just played the first game, scored three goals, that’s pretty promising. It’s a long season, we need players with different abilities.
"(Mohammed) Kudus has the spark and creativity, Wilson (Odobert) does that well, Mathys (Tel) can play different positions.
"We have two good strikers in Dom (Solanke) and Richy, Brennan (Johnson) the deep runner. We have variation up the pitch, but again we’ll look out there for someone who can strengthen, but that’s in all areas."