His one-man show at Old Trafford in October 2016 drew the praise of United boss Jose Mourinho, but he made only three league appearances last season after being ranked as the Potters’ number two keeper behind Jack Butland.
Stoke were eventually relegated under Paul Lambert after the Scot replaced former United striker Mark Hughes in charge at the bet365 Stadium.
And United have been on the lookout for a suitable third-choice to complement David de Gea and Sergio Romero after deciding to give Pereira the opportunity to play games elsewhere.
Pereira played only 12 minutes of senior action last season in coming on as a late substitute against Burton Albion in the League Cup, and his regular involvement in matchday activity with the first team also reduced him to only two reserve outings.
That has resulted in the 22-year-old, who Mourinho regards as the best Portuguese goalkeeper of his generation, asking to be allowed out on loan in order to gain more experience. A number of clubs across the continent are thought to have sounded out United regarding a short-term deal for the former Rochdale and Belenenses loanee.
United also bade farewell to Sam Johnstone this week after the 25-year-old completed a £6.5 million switch to West Bromwich Albion.
His fee could eventually rise to around £10 million depending on his achievements at The Hawthorns.