The England international is reported to be on the verge of a £25m switch to Anfield from Southampton, with some media outlets claiming that a deal has already been struck.
But the Liverpool manager remained coy when questioned about the rumours linking the Reds with the 26-year-old.
Asked if Lallana would be Liverpool’s next signing, Rodgers replied: “I wouldn’t tell you.
“I would love to stand here and tell you. We still have signings to make to ensure we have the squad strength to cope.”
Rodgers did however insist that his transfer activity is far from over following the arrival of Rickie Lambert earlier in the window.
“We’ve targeted players, we’ve signed some and we’ll have more signings to come over the course of the pre-season,” he added.
“The idea is by the end of August we’ll have the squad together and it will be a really exciting time for us next season.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news