You can convert CorelDraw CDR graphics to Adobe Illustrator AI vecror file format using UniConvertor or similar program. However, as CorelDraw .cdr is proprietary and closed format and the end result won't most likely be perfect. The newer cdr format it is, the worse the odds for successful conversion are.
If you have booth programs - CorelDraw and Adobe Illustrator, you can also export to AI or PDF directly from CorelDraw and then open or import this file to Adobe Illustrator. You can exchange graphics parts through clipboard or export to other common vector graphics and then import it to Illustrator.
The question is how is artwork created in Corel and how do you export it. If you need to work also with layers, go to Tools ► Object manager and create all layer you need. Each object will be stored in the layer you select. Illustrator will preserve all the layers from CorelDRAW. When you export your artwork as Illustrator file format, select the right Illustrator version you have, not only the default version suggested by Corel.
There are many versions of CorelDraw graphic suite and many versions of these graphic formats. We recommend to use latest versions of booth software. At the time of writing, latest version of CorelDraw X7 supports saving to Adobe Illustrator file format. Easily go to File -> Save as.. and export cdr graphics to ai.