The 22-year-old Batshuayi is expected to sign a five-year contract with the Premier League side for a transfer fee of about 40 million euros (£33 million), the newspaper said without citing sources.
Marseille had reached a deal with another Premier League club, Crystal Palace, earlier this week but Batshuayi turned down the offer, L'Equipe wrote.
Batshuayi had to pass a medical in Bordeaux, France, where Belgium are based for the European Championship finals, and Chelsea could announce the deal later on Wednesday, according to the French newspaper.
Batshuayi who joined Marseille from Belgian side Standard Liege in 2014, scored 23 goals in all competitions last season.
Belgium face Wales on Friday in Lille for a place in the semi-finals of Euro 2016.
Batshuayi had been due to talk to the media at the national team's base at Le Hallian on Thursday, but another player took his place at Marseille's request, Belgium officials said.
HIGHER LEVEL
Asked how the news had affected the camp, defender Jordan Lukaku said: "Is it official yet? The move didn't affect the group at all. All the guys are happy for him, and it's good for the national team that we have more players playing at a higher level."
Belgium coach Marc Wilmots said it was a good thing players were talking about transfers, with Club Bruges defender Thomas Meunier having been linked to French champions Paris St Germain.
"It sends the message that clubs are taking note of the fact that they are growing. Yesterday afternoon Michy and Thomas talked with me and took some time for themselves to focus on the issues they have with the clubs to clear their heads."
Wilmots also noted the transfers were not yet official.
"This morning everyone was back on the pitch for training and everyone has a clear head and that is the reason I have given my players a free afternoon," he said.
(Writing by Patrick Vignal; Reporting by Angus MacSwan, Editing by Clare Fallon and Ken Ferris)
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