Sky Germany reports that Ten Hag is being considered by the Bundesliga club if they choose to sack current manager Marco Rose amid a bad run of form.
Leipzig have lost five out of their last six matches in all competitions.
They recently lost 5-1 at home against Wolfsburg in the Bundesliga.
Leipzig currently sit in fourth position on the Bundesliga table, but Rose must turn this run of results around or faces losing his job.
The report added that former Benfica manager Roger Schmidt is also believed to be a candidate for the RB Leipzig role after leaving the Portuguese club at the end of August.
Recall that Ten Hag was sacked as Man United manager in October after a poor start to his third season at Old Trafford.
The Dutchman was replaced by Ruben Amorim who arrived from Sporting Lisbon.
