There is a sort of star called a Brown Dwarf. Generally they are just large enough to begin to undergo fusion (deuterium fusion), but not large enough to fuse hydrogen. These are 13 times larger than Jupiter to 65 times larger than Jupiter.
The lowest mass star observed to support hydrogen fusion is about 7% the size of our sun. Jupiter is 0.1% the size of our Sun, so 70 Jupiter masses would therefore be massive enough. Since we know that 65 times the mass of Jupiter is not big enough to fuse hydrogen and that 70 times is big enough, something greater than 65 times but possibly less than 70 times the size of Jupiter would be considered a star.