Krasic joined Juventus from CSKA Moscow in 2010 for around £12 million but is on the verge of leaving the Serie A champions after featuring just seven times under manager Antonio Conte last season.
Tottenham are believed to have made an attempt to land the Serbian winger in the January transfer window, but could not agree terms on a loan move.
Liverpool have previously been linked with a move for the 27-year-old but now appear to be upping their interest after making contact with Juventus over a season-long loan deal, although the Italian club are said to be only interested in a permanent switch.
Despite previous reports, Goal.com claim that there have been no talks between Liverpool and Juventus over Luis Suarez, and that the Uruguayan is not involved as part of a deal for Krasic.
The Reds are on the lookout for cheaper transfer options this summer after spending over £100 million in the transfer market in the last 18 months, with Krasic fitting that criteria - although Juve are keen to recoup as much of the fee they paid out two years ago as possible.
Spurs are believed to still be interested taking Krasic to White Hart Lane and could still challenge Liverpool for his signature, but are currently occupied in landing other summer targets, namely Ajax defender Jan Vertonghen and Marseille forward Loic Remy.
Newly promoted Reading are also interested in Krasic, but it is thought that Serbian will not consider a move to the Royals.