No. do not under any circumstances claim your yet-to-be-reimbursed expenses on your 2019 return. That's because when you "do" get reimbursed, the amount you are reimbursed will "NOT" be included on "ANY" W-2 that you receive.
If you claim the as-of-yet-unreimbursed expenses on your 2019 tax return, then you will be "required" to claim the reimbursed amount as "taxable income" on your 2020 tax return next year. That has the potential to raise your AGI to the next higher tax bracket. So just leave well enough alone.