The Switzerland star is expected to leave the Britannia Stadium this summer, as he is not interested in playing Championship football.
Reports in Swiss publication Blick have suggested he can go for as little as £12 million, so a whole host of teams will no doubt be queuing up to try and secure his services.
Everton must ensure they are at the front of that queue and one way they can do so is to offer Stoke the chance to bring in one of their current flock.
This season has seen England under-21 international Kieran Dowell have an impressive campaign with Nottingham Forest. In the first half of the season, he was a regular in the City Ground first-team. Despite tailing off after the new year, this season will be considered a success for the youngster.
Plenty of Everton fans would love to see Dowell get a first-team chance next season. However, if Shaqiri is to arrive at Goodison Park, that looks a difficult scenario for the young man.
So instead, Everton should offer Stoke a sweetener, by seeing if they would like to take Dowell on loan for the season.
The attacker would be a direct replacement for Shaqiri and has shown he can cut it in the Championship with Forest this season.
Another year playing in the second tier, with a team expected to challenge for promotion, would be good for his development. Meanwhile, Everton would get Shaqiri and keep Dowell on their books in the long-run as a future first-team star.
It would represent good business all around for all three parties.
Hopefully, it is an idea that can be put into practice by both Everton and Stoke this summer.