The Saints striker would be a surprise move for either side.
The report claims that both Jurgen Klopp and Mauricio Pochettino are fans of the Republic of Ireland international who has two-and-a-half years left on his deal at St Mary's.
Long, who joined Southampton in August 2014 from Hull City, is a striker who divides opinion.
He has lightning pace and is a tireless worker but it would be fair to say his finishing sometimes leaves little to be desired. However those former attributes rate highly in Klopp and Pochettino's books.
But he can put in the odd wonderful performance against big teams - just ask Arsenal or the Germany national side.
Long, who is likely to be on his way to the European Championships with Ireland in the summer, is not believed to be pining for a move from Southampton but if Liverpool and Tottenham came calling he may have to reevaluate that stance.
Liverpool are currently short up front because of injuries to Daniel Sturridge and Danny Ings whilst Spurs need striker cover for Harry Kane and Heung-min Son.
However it remains unlikely that either side will want to go for Long, with higher profile targets said to be on the radar.