Blomqvist made just 18 appearances for Everton before being released by new Everton boss David Moyes at the end of last season.
Steve McClaren is well aware of the Swedish wingers capabilities after their association at Man. United, although the Swede had a disappointing time with several niggling injuries.
Blomqvist said: "I will be staying in Middlesbrough for a few days and practice with them and we will see what happens. We have been in contact for the last four or five months."
He went on to say "A while ago, Steve McClaren proposed that I should come over to get a feeler - practice with the side and look at the town. Then, we shall see how it ends. If it feels good, we will be talking about it at the end of the week. But since they are inviiting me to the club, there is of course an interest from their side. And I would like to stay in England for a few more years."
Blomqvist is just another name in a long list of maybe's as Steve McClaren steps up his search for new blood before the season kicks-off on 17th August.
Boro officially announced today that they were interested in Real Madrid's Cameroon defender Geremi, although spokesman Dave Allan stressed that any deal would be subject to a successful work permit application and the player passing a medical.
For the record his full name is Geremi Sorelle Ndjitap Fotso.