The striker has apparently decided he needs to leave the Gunners to fulfil his potential.
The Sun claim Leeds are looking at Akpom as a potential replacement for Chris Wood after he left for Burnley in a £15m deal.
The 21-year-old has had loan spells at Brentford, Coventry, Nottingham Forest, Hull and Brighton.
He has played for Arsenal just four times, despite making 67 senior appearances for various clubs.
Brendan Rodgers also wants to bring in Akpom to compete with Mousa Dembele and Leigh Griffiths for a striking role.
Akpom has represented England at both Under-16 and Under-21 level.
Arsenal have various strikers at the Emirates with Alexandre Lacazette, Olivier Giroud and Danny Welbeck all well clear of the youngster in the pecking order.
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For that reason the Gunners could well grant Akpom his wish and let him leave before the transfer window slams shut on August 31.
Leeds will want to replace Wood quickly as they look to continue their strong start to the Championship season.
The Whites are fifth after four games and have yet to lose this season.
Their next match is against Newport tomorrow night in the Carabao Cup before they face Nottingham Forest in the Championship on Saturday.
