Liverpool boss Jurgen Klopp wants to see four first teamers sold this summer.
The Times says there could be more than the quartet cashed in, as Klopp seeks to perform a clearout.
Among those to be sold are Simon Mignolet, Daniel Sturridge, Danny Ings and Harry Wilson.
Liverpool are looking to recoup some funds in order to fund moves for other stars.
Alisson is a target and would require a huge bid of around £60m to dislodge him from Roma.