Liverpool had initially been linked with a move for the Brazil global but they are understood to be unwilling to meet Roma's valuation of the player, who kept 17 clean sheets for Roma in Serie A last term, the second-highest total behind Napoli's Pepe Reina.
Reports in Spain claim both clubs have opened negotiations for the 22-year-old, who is looking for more playing time.
If Brazil go deep in the World Cup, it's likely that Roma will raise their asking price, given the amount of hype that will surround Alisson. Alisson is believed to be the Merseyside club's first-choice target, but the Reds now face stiff competition from Chelsea in his pursuit.
A move to Stamford Bridge could pave the way for Chelsea goalkeeper Thibaut Courtois to move to Real Madrid. Many rumours have stated that Chelsea have now made a decision to put him on the market and will be willing to sell him if an offer of over 50 million arrives for the Belgian shot-stopper.
Meanwhile, signing a top-class replacement for Courtois is also imperative, with Alisson a viable, long-term target.
And the 26-year-old reiterated his feelings about a possible move.
However, negotiations between the two clubs have been hard and Real Madrid are unwilling to match Roma's €70m asking price for the Brazilian goalkeeper. Today, Chelsea are closing-in on Alisson....