Unai Emery is angling for a number of new faces after his side capitulated at the end of last season.
While bringing in a winger is a priority, Emery has jumped at the chance to sign central midfielder Ceballos.
With Aaron Ramsey having quit the Emirates on a free transfer, the Spain international could be an ideal replacement.
The Gunners have been heavily linked with Ceballos and reports have suggested that Real are willing to let him join Arsenal on loan.
But it has since emerged that a cash bid has been made as Arsenal plot a permanent signing instead.
And Italian journalist Nicholo Schira says all that’s left is for the two clubs to define the final details of the transfer.
“#Arsenal is near to close the arrival of #Ceballos from #RealMadrid,” he tweeted on Monday.
“They must define the last details in the next days. #transfers #AFC”
beIN Sports correspondent Tancredi Palmeri says Real Madrid have made a significant demand as proceedings take shape.
“Arsenal have offered €30m to Real Madrid for Ceballos,” Palmeri tweeted. “Real Madrid insisting for putting a buyback clause at €40m.”
Ceballos impressed this summer as Spain Under-21s won the European Championships.
And Sky Sports reporter Kaveh Solhekol believes his performances may have convinced Real to want to hang on to him.
“Ceballos still believes he can have a major impact at Real Madrid in the future – hence he wants to go back,” he told the Transfer Talk podcast.
“But for now, he wants to be happy, he’s been quoted as saying. And what would make him happy is playing 40 games next season, and he believes he’ll be able to get that at Arsenal.
“It just needs the final approval of the Real Madrid boss Zinedine Zidane before it officially gets over the line.
“We were of the understanding perhaps Real Madrid wanted to do a permanent deal, and bring in some money, because they’ve spent a lot in this transfer window.
“But I think their minds were changed when they saw Ceballos perform so well at the European Under-21 Championships.”