Bishop caught the eye with his performances for Stanley last season and two of Accrington’s League One rivals want to secure his services.
Accrington are prepared to sell if the price is right and MK Dons are making a fresh bid for Bishop, though it is claimed to be substantially below Stanley’s valuation.
Portsmouth meanwhile watched Bishop play in a friendly against Stoke last week as they further put him under the scanner.
Danny Cowley’s side are expected to compete with MK Dons for the signature of the 25-year-old.
Portsmouth are keen to continue to add to their attacking options following the arrival of Joe Pigott and want Bishop.
Accrington plucked Bishop from non-league and he has shone in League One for the club.
Bishop has reached double figures in terms of goals in both seasons in which he has been on the books at Accrington.
