Munster already boast a total of six Lions in their current squad, with Keith Earls, John Hayes, Donncha O'Callaghan, Ronan O'Gara, David Wallace and skipper Paul O'Connell part of the furniture in Cork and Limerick.
Flutey, who started the Lions' third-Test win over the Springboks in July last year, is currently plying his trade with French outfit Brive.
The New Zealand-born star only moved to the Top 14 following the Lions' summer tour of South Africa but he could be on his way out after just one injury-plagued season in France.
Flutey has also been linked with former club London Wasps, coached by Lions defence coach Shaun Edwards, but it appears that the transfer fee demanded by Brive will be too much for the English side.
The 30-year-old may have to pay his own way out of the final year of his contract but Munster are thought to be offering him a three-year deal to ease that burden.