The actors have apparently been dating since October 2011, with recent rumours suggesting an engagement or marriage between the pair.
However, Star magazine reports that friends close to the couple claim that the relationship is on thin ice, due to Lively's desire to tie the knot, though Reynolds is "absolutely against getting married".
Reynolds was once engaged to singer Alanis Morissette, and recently divorced Scarlett Johansson after two years of marriage.
A source close to the pair told the publication that their ten-year age gap is also an issue, adding: "Many of Blake's friends are younger than him, so it makes hanging out in groups incredibly weird."
Despite the claims, the pair were spotted together on Sunday (September 2) in Venice, where they attended a party hosted by Gucci at the 2012 Venice Film Festival.