Ekstrand was released by Watford in June after suffering bad injury problems.
Leeds United have already completed the signing of one Swedish player this week with the arrival of Marcus Antonsson, but according to the Bristol Post, referencing a report from the Guardian, they are also working on a deal to bring defender Joel Ekstrand to Elland Road.
Garry Monk has got his summer transfer plans underway in earnest with the signing of striker Antonsson on Tuesday, and having bolstered his attack he is now expected to look to strengthen other positions ahead of the new Championship season.
The Whites defence was perhaps the area of the side to come under the most scrutiny last season with the likes of Giuseppe Bellusci coming in for criticism from supporters, and with Scott Wootton having been released in May the backline undoubtedly needs more depth.
Ekstrand was let go by the Hornets after failing to make a single appearance last term in the aftermath of a cruciate ligament injury suffered in March 2015.
Before that problem, however, he had been an important player for the London side after signing from affiliated club Udinese in 2012, making 75 appearances in his first two seasons and remaining a regular when fit until his injury 15 months ago.
The 6 foot 2 inches 27-year-old undoubtedly has the class to succeed if he can settle back into life as a regular Championship player, but Leeds are thought to have competition from other second-tier clubs such as Bristol City and Reading for his signature.