Jacob Murtagh in the Mirror reported the defensive duo's potential return to action, with both having missed out on representing their countries during the recent international break.
Croatia international Lovren, 27, picked up a knock in Liverpool's last outing against Swansea City, while Clyne missed out on facing Malta and Slovenia with England.
Given that Liverpool's back line remains the weak link in their side, manager Jurgen Klopp will be desperate for Lovren and Clyne both to be available for the United clash at Anfield as the Reds go for a fifth Premier League win on the bounce.
Clyne is Liverpool's undisputed starting right-back, and there is little genuine cover for him in the position.
Meanwhile, despite Klopp adding Joel Matip and Ragnar Klavan to his centre-back options in the summer, Lovren remains a key part of the defence and has started five of the Reds' seven Premier League matches in 2016-17, per WhoScored.com.
The Croatia international is an increasingly reliable presence at the back, and given Liverpool's overall weaknesses in defence, he is something of a stalwart in the defensive line.
There is cover available for him, with Matip, Klavan, Mamadou Sakho and even Lucas Leiva able to drop into the middle of defence.
But Klopp will be delighted to see Lovren return to fitness as Liverpool look to continue their excellent start to the new campaign.