The 29-year-old recently left Manchester City to join Everton on loan. The deal includes a £50 million buy option, according to a report from The Athletic.
The same report adds that despite the interest from Celtic, Grealish 'never seriously considered a move to Scotland'.
Brendan Rodgers, the Celtic manager, is on the hunt for attacking reinforcements.
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With the Champions League play-off against Kairat Almaty on the horizon, Rodgers has limited options on the flanks, with Yang Hyun-jun, James Forrest, Daizen Maeda, and Marco Tilio being his only choices.
Following Celtic's 2-0 victory over Aberdeen, Rodgers was asked about potential new signings.
He said [Sky Sports]: "Look, I think that I've got no news now at this very moment on where we're at.
"Our job between now and the end of the window is to make Celtic the very best that we possibly can.
"In the meantime, we'll continue to develop the players that are here and improve them."
Rodgers added: "Of course, I want Celtic to live in the very best possible place that it can be.
"And for me, that'll be us signing more players at the top end of the pitch.
"But I can't magic them in there, and if they're not there, then we'll work with the players that are there and make them the very best that they can be.
"We know what we need to strengthen."