Liverpool's need for a new goalkeeper stems from a season in which both Loris Karius and Simon Mignolet failed to hold down the number one shirt.
Both goalkeepers endured inconsistent seasons, with Karius eventually costing Liverpool the Champions League after two blunders in the final against Real Madrid.
The Liverpool Echo are reporting that despite being linked with both Pope and Strakosha, Klopp is not plotting a move for either keeper.
This news leaves the Merseyside club in the unenviable position of still having to find a new number one ahead of the new season.
The Reds had been linked with Roma stopper Alisson, but appear to have been priced out by the Italians, with the club expecting a fee somewhere in the region of £70m. It's understood that although Liverpool had made the Brazilian their number one target, Spanish giants Real Madrid are now the frontrunners.
Real president Florentino Perez has reportedly made replacing Keylor Navas a priority this summer, and Alisson appears to fit the bill perfectly. The Spanish club had previously been linked with David de Gea and Thibaut Courtois, but with Liverpool unable to match Real's financial might, Alisson is seemingly the choice to take the number one spot at the Bernabeu.
It remains unclear who Jurgen Klopp wishes to make his new number one at Anfield, but having ruled out Pope and Strakosha, Liverpool fans will be hoping the club gets their business done sooner rather than later.
The acquisitions of Fabinho and Naby Keita suggest the Reds are plotting a title charge in the 2018/19 season, but in order to do that they'll need a dependable goalkeeper between the sticks.