Ruben Amorim is said to be the leading candidate to take over at Liverpool after Xabi Alonso said that he would stay at Leverkusen.
According to journalist Ben Jacobs, Brentford's Thomas Frank might also be considered by the Reds.
"They are trying to get a final shortlist and, therefore, there will be more than one name on that final shortlist," Jacobs told Give Me Sport.
"Julian Nagelsmann scored very highly on Liverpool's data. He obviously isn't available until after Euro 2024, but he could still be one to watch.
"Roberto De Zerbi hasn't been approached. I know we hear a lot of hype about him potentially moving, and he has said on record that his contract situation and his future at Brighton is yet to be resolved, but there hasn't been any contact yet between Liverpool and De Zerbi.
"Thomas Frank is admired as well. It remains to be seen whether he progresses to the final stage."
The 50-year-old has been in charge of Brentford since 2018. He guided them to promotion to the Premier League in 2021 and has so far kept them in the competition despite operating on a comparatively low budget.
