Rovers boss Sam Allardyce is believed to have Guti, 33, on his summer shopping list and talks between the two parties have been held.
The skillful midfield kingpin is likely to see his chances limited under Jose Mourinho and he is believed to be keen on a move to England.
Allardyce is on the hunt for a striker and James Beattie, Frederic Piquionne and Kris Boyd have all been linked with a moved to Ewood Park, but Guti could well be the first arrival of the summer.
Vekic said: "It is possible. Little talks have gone on and, while there is nothing happening at the moment, it is possible."
Source: Team Talk
Source: Team Talk