The Marseille marksman has emerged as one of Europe's hottest properties after netting 26 times for the Ligue 1 side in all competitions last season, according to ESPN.
The Mirror reported last week that the 22-year-old was looking for an estimated £100,000 per week to join Tottenham as a move to White Hart Lane seemed to be gathering momentum.
The report goes on to suggest that Batshuayi would favour a move to White Hart Lane but that West Ham United are closer to tabling a satisfactory offer for the striker.
West Ham arguably need a prolific goalscorer more than Tottenham, with Harry Kane netting 25 times in the Premier League last season to win the Golden Boot.
Andy Carroll and Diafra Sakho - who is expected to leave West Ham - are Slaven Bilic's only out-and-out strikers and neither are going to score enough goals to propel the Irons to a new footing in English football.