The 30-year-old joined the Reds on a free transfer last summer from Standard Liege but struggled to hold down a regular place.
He made just one start after Kenny Dalglish took over for the second half of the season and did not make the squad for the final four months of the campaign.
The Serbia international's wife has already expressed her preference to return to Belgium and it appears Anderlecht have made their move.
"We're currently negotiating with Jovanovic but we couldn't achieve an agreement (yet)," a spokesman for the Belgian side told BBC Sport.
"We're very much interested and the player would like to come.
"Anderlecht are due to contact Liverpool today."
Jovanovic is one of a number of players surplus to requirements at Anfield and has been told he can leave.
The stumbling block so far has been finding a club willing to come close to matching the player's current wages, which are believed to be around £60,000 a week.