The Reds have been heavily linked with a move for Thiago, with midfielder said to be keen on a move to Anfield following seven hugely-successful years at the Allianz.
Liverpool were expected to splash the cash on new faces this summer following three relatively quiet transfer windows, But the coronavirus pandemic's impact on football clubs and their finances has potentially shelved those plans, including a move for Thiago.
Klopp has reiterated in the past few months that a big-money move would represent a significant risk for the club, who are unable to plan ahead or forecast their financial status due to uncertainty surrounding fans returning to stadiums and TV rights payments.
When directly about the possibility of signing Thiago, Klopp told ServusTV: “There are a lot of interesting players out there, but if someone is interesting for us I can´t say right now.
“Due to COVID, you have to think five times about what you can and what you can´t do. We always have to pay attention to the financial aspect.
“We don´t know how much money will come in. Nobody knows, but it seems like some other teams have a more positive outlook on the future. If you take a look at Chelsea, for example, yeah!
“But I am very happy with my team right now. If something transfer-related will happen, we have to see.”
Additionally, the Telegraph's Chris Bascombe reports that Wijnaldum will not be offered a contract extension to his current deal, which runs out at the end of next season.
While Bascombe suggests there are no plans for Wijnaldum to leave the club this summer, he could be allowed to depart should a suitable bid be made for his services.
Liverpool have signed left-back Kostas Tsimikas from Olympiakos so far this summer. Further incomings are expected but it is clear Klopp is willing to stick with his current squad if no suitable additions can be found.