Sunderland target Diafra Sakho is reported to have refused to travel with the West Ham United squad on their tour of Austria.
Crystal Palace, Watford, West Bromwich Albion and Sunderland are all understood to be tracking the striker, who is looks set to leave West Ham this summer.
The striker, subject of a failed £11million transfer bid by Sunderland back in June, handed in a transfer request earlier this month.
Sky Sports report Sevilla and Hamburg have also both enquired about Sakho's availability.
Sakho is keen to be reunited with Allardyce after his spell working under him at West Ham.
But his potential move to the Stadium of Light would be in jeopardy if the FA decide to offer Allardyce the England job, following talks in Cheshire last week.
Allardyce remains the favourite for the England job, with Hull City boss Steve Bruce and AFC Bournemouth boss Eddie Howe also being considered along with USA coach Jurgen Klinsmann.