This is an uneasy question. Almost all of the solvents have some hazard, from fire cautions to healt problems, some of them include both. Depending on the polyolefin you are dealing with, there are some solvents you can use. I recommend to look at the Polymer Handbook for solvents and non-solvents -upon your polyolefins-, then google for the solvents MSDS document, a cross-check will be very useful.

Actually, there is an easy answer to this question too... Ionic liquids as solvents.. though these are pretty expensive.

I seriously doubt that ionic liquids would ever dissolve polyoelfins, bein low olarity materials ...

As the phrase says: "like dissolves the like", in the case of polyolefins, the usual solvents are petroleum-based. Even thought, water is considered as an universal solvent, such liquid will eventually dissolve even polyolefins, the main problem is that such phenomenon won't happen while we are alive...

There are no common solvents that dissolve polyolefins at room temperature. However, you can use decalin (decahydronaphthalene) or decalin-cyclohexane mixture to dissolve LDPE, HDPE, a-PP, i-PP at 130-140 deg C. Cooling the mixture while stirring gives a clear solution at 50 deg C (for HDPE and LDPE).