The Daily Echo says Hasenhuttl has made it clear that he's happy at St Mary's and will start talking about an extension once he feels his side are safe from relegation.
Saints' hierarchy are also relaxed about this view and see it as the sensible option.
Hasenhuttl also wants to repay the club for the faith they put in him after his team lost 9-0 to Leicester last year.
He initially joined on a two-and-a-half-year deal in December 2018 when he replaced the sacked Mark Hughes.
His remit was to ensure Saints maintained their Premier League survival after Hughes left the club in a precarious position.