Plans to clone the thylacine were widely discussed in the media, starting around 1999; see first story, second story, and third story. However attempts by the Australian museum to create a thylacine genomic library were unsuccessful: first story and second story. A news story in May 2005 reported that the project had been picked up by another group.
The sticking point for resurrecting the thylacine is likely to be the absence of a sufficiently close living relative to supply eggs and act as a surrogate. If, however, it were somehow possible to boot up the thylacine genome in a living cell, then things would be looking up. The interesting thing about marsupials as opposed to other mammals is that pregnancy is so short, usually lasting just a matter of weeks. This means the thylacine's dependence on a surrogate mother would be much less than for mammals with a long gestation period. Once born at only a few millimeters in size it might be possible to feed a baby thylacine milk in an artificial pouch.