Spurs, who beat Burnley 3-0 on the opening weekend of the season, travel to Manchester City on Saturday (12:30PM BST).
With the transfer window set to close on 1 September, Frank remained confident of adding to his squad.
“We are in the market and we will look to strengthen the team,” he added.
“We have a good squad and good players [but] 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. Every club wants to sign players as early as possible, but it’s not that easy.”
Frank said striker Richarlison, who netted twice in the win against Burnley, is set to stay at the club.
The Brazilian, 28, had been linked with a move to Palace in part-exchange for Eze.
Arsenal host Leeds United on Saturday (17:30 BST), with Eze expected to complete a medical with the Gunners over the weekend.
But head coach Mikel Arteta said on Friday: ‘I have nothing to comment.
“You know I can never talk about a player that’s not part of our group or club yet.”
