The Sun says the Gunners reckon they have seen off competition from Manchester City for the Championship whizkid.
The Premier League leaders hope to land the 18-year-old for £2m.
Addicks interim boss Karel Fraeye insisted Lookman is not leaving The Valley.
"Ademola is on a two-and-a-half year deal already," Fraeye said last month.
"We are doing what we have to do. I think we are very close to where we want to be.
"Ademola has just started first-team football. He's started very well but he's got so many steps to take.
"I'm sure he won't be sold in January and will be here in the long-term.
"He's a smart boy and I think Charlton is a good club for him. If he is looking for a club to develop at, he's at the best club for him and he knows that."