The Sun believe that Liverpool intend to take advantage of Spurs chairman Daniel Levy's attempts to play hardball over a deal for the midfielder by swooping in under his nose with a bid.
Spurs have long been considered the favourites to sign the 22-year-old but now face the risk of being gazumped by Liverpool, with the London club thought to be unwilling to pay more than £20m.
Recent reports also suggest that Levy is attempting to take advantage of Villa's recent financial woes by holding out on offering any more money for Grealish - however, this plan now looks to be at risk of backfiring as Liverpool prepare to offer more money for the player.
Jurgen Klopp has already added two midfielders to his ranks this summer, with deals for RB Leipzig's Naby Keita and Monaco's Fabinho already tied up - nonetheless, the Liverpool manager may look to further bolster his squad with the addition of Grealish.
Everton and Leicester have also been linked with a move for Grealish but this seems unlikely, with neither side capable of offering Champions League football and Leicester having now signed Norwich City midfielder James Maddison.
Grealish made his debut for Aston Villa in 2014 while the West Midlands club were still in the Premier League. He made 31 appearances last season and has become a key player for Steve Bruce's side.
However, with Villa failing to secure promotion back to the top flight last season after defeat in the play-off final against Fulham, Grealish could now be set to look for pastures new this summer.