The tissues come from a femur of a Tyrannosaurus Rex fossil, known as MOR 1125, found in the northwestern state of Montana, the researchers said in a report published on Friday in Science magazine.
It measures 1.07m and comes from an 18-year-old Tyrannosaurus.
The fossil was broken when it was removed from the site, allowing researchers a clear view of its interior, North Carolina State University palaeontologist Mary Schweitzer and her colleagues said.
"The vessels and contents are similar in all respects to blood vessels recovered from ostrich bone," she said.
If they can manage to isolate certain proteins in the tissues, Schweitzer said, "then perhaps we can address the issue of the physiology and life of the dinosaur".
"Tissue preservation to this extent has not been noted before in dinosaurs," she said.
"If we have tissues that are not fossilised, then we can potentially extract DNA. It's very exciting," said Lawrence Witmeyer of the same university.
In Steven Speilberg's 1993 Hollywood blockbuster Jurassic Park, based on best-selling author Michael Crichton's novel, scientists recreated dinosaurs by cloning their DNA.