Football Insider say the Danish star is ready to move to Merseyside and become the fourth Everton signing of the summer window so far.
The Toffees have already brought Jack Harrison back for another season-long loan, while they have added new signings Tim Iroegbunam and Iliman Ndiaye on permanent transfers.
Rumours that Lindstrom was the next target have gathered pace in recent weeks and now he and Napoli could be about to conclude a deal to join the Blues.
Everton needed more pace, width and goal threat before the transfer window opened, and then with Arnaut Danjuma and Harrison both returning to their parent clubs the options out wide looked particularly threadbare.
So, a move for Lindstrom fits the profile of the sort of player that Sean Dyche has been keen to add to his small squad.
According to this report, the Toffees will agree a loan deal for the Dane with probably an option to buy outright next summer to be included.
Obviously, a loan makes financial sense for the cash-strapped Blues, especially now the proposed takeover by The Freidkin Group has collapsed leaving fresh uncertainty about the club's future.
However, Lindstrom's form has been poor since his move to Napoli from German football where he had previously made a decent impression.
Last season he failed to score a single goal in twenty-two games for the Naples side, although to be fair most of his appearances were from the bench.
His main position seems to be operating on either flank but he might also be able to play off the lone striker too.
The Serie A outfit seem prepared to cut their losses and let him move on in the hope he will find better form on Merseyside and that Everton will then cough up for a permanent deal.
Of course, that will depend on how well he does in the Premier League and also presumably whether the Toffees have finally got a new owner installed by the time next summer's transfer window opens.