The Lithuanian has been identified as the man the club want to install as No.2, although Gary Locke remains on the coaching staff following the departure of Paulo Sergio.
It is not yet clear to what extent McGlynn was consulted on the expected appointment of Jankauskas. The 27-year-old served as assistant to Jose Couceiro – previously thought to be a candidate for the manager's job – at Lokomotiv Moscow last season.
Jankauskas is well known to Vladimir Romanov, the Hearts owner, having also played for FBK Kaunas before moving to Tynecastle on a loan spell during which he helped the club win the Scottish Cup in 2006, having also been at the club when McGlynn took charge of the side on an interim basis earlier that season. The club are thought to have already drawn up a contract following discussions.
McGlynn, who was named as the new manager this week, had been assisted by former Hearts player Paul Smith while at previous club Raith Rovers, although they will not be reunited at Tynecastle. Smith has instead been appointed as caretaker manager at Raith.
Another former Hearts player, Steven Pressley, has heralded the appointment of McGlynn. The Falkirk manager – who had been among the first names to be linked with the vacant post at Tynecastle – accepts that McGlynn is perhaps not the most glamorous name but has lauded the Edinburgh side for selecting a coach of substance.
"There are plenty of big names out there, foreign or otherwise, but behind the big names and supposed glamour is there a real substance?" said Pressley. "I would compare it to when Reading appointed Brian McDermott as their manager. There were many fans who would have thought he didn't tick the boxes, wasn't a big name for the supporters, but they are a Premiership football club now. In terms of substance and what he can give to Hearts Football Club, there is no argument against John. It is a terrific decision by Hearts and a great opportunity for John."