I would think something like Spoonflower would deal with this sort of thing, you might also contact local T-shirt type shops. Maybe a little harder to find someone willing to work from the actual jersey but I wouldn't think too much. I'd do searches on transferring photos to fabric or similar to see if they would work with the jersey.
Someone would need to scan the original signatures/jersey. You can take that scanned/digital image and easily get that printed. My little $200 home laser jet printer has a scanner bed and scans in color but only prints in black and white I do a surprising amount of quilt work at my local office store (happens to be Staples) and often use their scanning abilities.
Back a decade or two ago, we did a lot more with copiers and transfers and printing on treated fabrics (which are often carried at the office supply stores and not just craft stores). Those had various success rates depending on what type of printer you had, what products did you use. The issue with transfers and copiers is making sure the signatures were legible (most copiers have a mirror image button to deal with that). Fewer issues for direct printing, but sometimes it comes up.
From what I'm hearing (haven't done it myself) the quality and dye retention of services like Spoonflower are great!