The teams will meet across the next two weeks in the third qualifying round with the winner progressing to face Robbie Neilson’s men across two ties.
What can Hearts, who are at home in the second leg, expect from the two teams?
The Swiss Super League champions are favourites to come through the tie with Linfield, but their title defence has started very poorly. They currently sit bottom of the table after three matches, having lost twice and drawn one.
There have been two key changes from the side which won the 2021/22 league 14 points ahead of Basel.
Manager André Breitenreiter was instrumental in taking the team from one which had narrowly avoided relegation the previous season to champions. Much of that came down to the way the team attacked with pace, not concerned about playing a possession game.
Breitenreiter has moved to Hoffenheim and been replaced by ex-Austria boss Franco Foda, while they have lost last season's 20-goal top scorer Assan Ceesay to Lecce.
They still have the likes of Nikola Boranijasevic and Adriàn Guerrero, who are key down the flanks, and Antonio Marchesano, who netted 13 times last season. In their five games so far, they have started with four different formations, while teams have allowed them to have the ball more in the league.
Zurich have also signed former Hearts winger Donis Avdijaj. The Kosovo international was a flop in the season the team were relegated under Daniel Stendel but scored five goals in 18 Austrian Bundesliga matches last season.
This season, encouragement can be found in their Champions League tie with a very capable Qarabag side, only losing after extra-time.
The club have confirmed the game will take place at the 19,694-capacity Kybunpark in St Gallen if they face Hearts. A concert is being held in their Letzigrund Stadium on Friday, August 19, the day after the first leg is due to be played.
The Northern Irish champions raised plenty of eyebrows when they defeated Norwegian outfit Bodø/Glimt 1-0 in a Champions League qualifier in Belfast. They were brought back down to earth the following week in the return leg, losing 8-0, not helped by having a man sent off in the 20th minute.
Managed by former Rangers striker David Healy, famous for his exploits for Northern Ireland, the team are the most successful in the country and have won the last four league titles, the most recent by one point.
They have had to contend with their top scorer from last season, with former Motherwell attacker Christy Manzinga joining Hungarian side Zalaegerszeg.
Linfield are a team who favour a 4-2-3-1 formation and are pragmatic. On the European stage against stronger opposition they will concede possession. While last season in the league, Larne enjoyed a bigger share of possession and they were fifth for number of shots.
They outperformed their expected goals by eight and conceded eight fewer than they were expected to.
There are a few familiar SPFL faces in their squad. They have Daniel Finlayson on loan from St Mirren and Eetu Virtanen on loan from St Johnstone, as well as former Inverness CT and Greenock Morton midfielder Conor Pepper.
Their league season doesn’t begin until August 13.