The Swedish defender says he would be open to a move to a club as "historic and successful" as the Reds, but is currently focussed only on his national team
The 27-year-old is no stranger to the Premier League having signed for Wigan in 2007 under then-boss Steve Bruce, though his stay was brief and unsuccessful.
After leaving the Latics, the defender impressed during his time at Dutch club Groningen before earning a move to Serie A last year.
Now Granqvist has said the prospect of moving to the Merseyside club is one that appeals to him because of its tradition and success.
"I'm happy and I love Genoa, but of course I'm flattered by the interest of the Reds,” Granqvist told Swedish publication Sportbladet.
“It's a historic and successful club."
The burly centre-back remained coy on the rumours linking him with a move to Anfield however, insisting he is focused solely on the national team and happy in Italy.
“It has gone very well for me and I have got much positive feedback in Italy,” Granqvist continued.
"I honestly don't know much. I'm focused solely on the qualifying matches with the national team. We'll see what happens in the future."