I am working on building a headboard with a 10" wide panel that attaches to a curved leg. I am concerned that the panel will be restricted from moving due to the curve of the leg or create a gap between the leg and the panel. Does anyone have any suggestions on how to attach them panel to the leg? I would like to keep this as solid wood, if possible. I have attached a simplified drawing.
You can do it if make that panel veneer on a plywood substrate - then you can glue it into a dado, or use some kind of fasteners, or biscuits. Laying up panels is a skill you will not be sorry you learned.
You have nothing holding the curved vertical members together except the panel. As far as I can see - I could be wrong. If you are going to stabilize your design using A solid wood panel, it will more than likely crack, because you will have to lock that panel in in order to achieve the rigidity you need for the headboard.
I hate to say it, because I think I can see you are going for something minimal, but this design wants upper and lower stretchers if you need to use solid lumber.
If the central panel is solid wood and the grain orientation is vertical as you indicate in the Comments expansion will be side to side, not up and down, so there's no real issue with the attachment of the legs to it. There will be a potential issue between the assembled headboard and anything you want to fix it to (because it will change width during the year) but that's a subject for another Question.
You can of course minimise seasonal movement by selecting quarter-sawn wood for the central panel. As I touch on in this previous Answer the expansion of QS wood can be significantly lower than for a flat-sawn piece of the same species.
I know you indicate that you would prefer to use solid wood throughout but if the central panel is made from plywood or another board material you'll have no issues with movement to concern you.
Per your most recent comment, the center panel grain runs horizontal. In that case there will not be any horizontal expansion to consider and the legs will maintain the same positions relative to the top cross beam that connects this leg with one on the other side of the headboard. The panel will expand and contract vertically and the amount of movement can be calculated (see the "wood-movement" tag wiki for links to calculators). You can easily absorb and conceal that movement by providing shoulders on the panel's tenons stopping the tenon short of the end by 1/2" to 3/4" from the end. Make the dado it fits in longer than the tenon to allow expansion of the panel. The dado should stop short of the end of the shoulder to insure that the shoulder always covers the dado. Finally, glue the panel to the legs only at the center so that the expansion (up and down) in the leg dados can occur.
The "leg" (10" wide, headboard, I have to assume there are multiple "legs") is curved. Simplify your life on the panels and cut the slots in the legs "straight" and deep; making the panels either a trapezoid or a rectangle. Then borrow a standard trick from frame and panel and insert a couple of rubber balls in each slot, which help to keep the panel centered as it shrinks and swells. Make the panel sufficiently wide (and the slots sufficiently deep, plus a bit) that any expected shrinkage will not cause a gap.
Edit: (Grain was vertical in early comments, has now changed to horizontal) So, now that you've changed your mind on the grain direction, make the slots longer than the panel and glue and/or pin only the center of the panel, so that movement is possible without damage.