Luis Suárez is also a reported target.
Saido Berahino is supposedly on his way to White Hart Lane from West Bromwich Albion, with QPR's Charlie Austin also a reported target.
One reported target was the Marseille forward Michy Batshuayi but any hopes of a January switch look to have ended after the Belgian signed a new contract with the French side until 2020.
Manchester United striker Javier Hernandez has emerged as a reported target for Arsenal as they continue their search for a striker to provide cover for Olivier Giroud.
Even with his £15million man on the mend, Allardyce is likely to bring in at least one other forward during the transfer window with Monaco striker Lacina Traore a reported target.
Meanwhile, Huddersfield midfielder Adam Clayton, a reported target for the Seagulls, is set to join Middlesbrough.
Martinez also represents Malaga midfielder Isco, a reported target for the Blues.
Burnley's 22-year-old striker Jay Rodriguez, who scored 21 goals for the Clarets last season, is a reported target.
Wolfsburg's former Chelsea midfielder Kevin de Bruyne, 23, a reported target for Arsenal and Manchester United, is not interested in a move back to the Premier League.
Brighton boss Gus Poyet, another reported target, is also a possibility but the former Uruguay international and Chelsea midfielder would cost Wolves a "prohibitive" £2m in compensation.
Inter Milan have made contact with fellow Serie A club Genoa over the transfer of 22-year-old Croatian defender Sime Vrsaljko, a reported target for Arsenal.
