Origi, 22, was left out of the Reds' squad that made light work of Arsenal at Anfield on Sunday (27 August) and has only seen 10 minutes of action so far this season, with new signing Dominic Solanke, Daniel Sturridge and Roberto Firmino all ahead of him in the pecking order.
While he has not exactly disappointed since joining Liverpool from Lille in the summer of 2015, Belgian international Origi has never established himself in the first team and may decide to seek pastures new with the 2018 World Cup in Russia on the horizon.
Tottenham are believed to be interested in taking Origi from the Merseysiders as they seek to recruit adequate cover for Harry Kane, but Liverpool would be reluctant to help strengthen one of their perceived rivals for a top-four position.
Klopp has a wealth of attacking options at his disposal and may yet strengthen his forward line with Monaco's Thomas Lemar, but is opting to wait and see what the immediate future holds for Origi.
"We will see," Klopp told the Liverpool Echo."That's not something to talk about here. If players come in, I think it makes sense to think about what we do on the other side.
"They're obviously involved in this (the players). I'm not sure, we will see, you have to wait. No games now so I hope you can enjoy the next five or six days with all the rumours and all that stuff. I'm not looking forward to it but it's part of the game eh?"
Tottenham manager Mauricio Pochettino is eager to see another three players arrive in north London before the end of the transfer window, which closes on Thursday, but a move for Origi may be hard to negotiate due to Liverpool's presumed disdain to help a league rival.
Spurs are close to completing their third summer transfer, though, with Estudiantes defender Juan Foyth nearing a move to the capital.