The newspaper claims Ward will be allowed to speak to Leicester once Alisson's £68 million move from Roma to Liverpool goes through.
Alisson is said to be undergoing a medical at Anfield, where Ward is already one of three senior goalkeepers, alongside maligned duo Simon Mignolet and Loris Karius.
And while Leicester are not short of options themselves in the Welshman's position, the report adds his arrival could 'open the door' for Kasper Schmeichel to leave.
Schmeichel has been strongly linked with a move to Chelsea after impressing for Denmark at Russia 2018.
Ward moved to Liverpool from Wrexham six years ago but has only played three times for the Reds' first team, despite impressing in spells at Morecambe, Aberdeen and Huddersfield Town and earning four caps for Wales.
Would Ward be a suitable replacement for Schmeichel at Leicester?