The Championship club could be on the hunt for a new shot stopper after receiving an enquiry from Sunderland for Andy Lonergan.
Leeds are under no pressure to sell Lonergan – who arrived from Wolverhampton Wanderers last summer – and will only sanction a departure if they can source a replacement.
According to the Yorkshire Evening Post, Bogdan is a potential loan target for Elland Road chiefs.
Bogdan, 30, has not played a senior game since November 2016 when he suffered a serious knee injury while on loan with Wigan Athletic.
Leeds news: Sunderland talks over swap deal involving Andy Lonergan and mystery player
The Hungary international still has 18 months left on his contract at Anfield.
Bogdan is fourth in the Liverpool pecking order behind Loris Karius, Simon Mignolet and Danny Ward.
Sunderland target Lonergan – a proven performer at Championship level – has not played for Leeds since the 4-1 thrashing at Wolves in November.
He wrestled a place in Thomas Christiansen’s team from summer arrival Felix Wiedwald in October but poor performances in the defeats against Brentford and Wolves resulted in him returning to the bench.
Leeds also have 21-year-old keeper Bailey Peacock-Farrell on the books.