I just started a new job.  As with most salary positions, I was quoted
a fixed salary when I signed up.  Within a couple days of arriving,
the owner offered to pay a sum of money every month that would be
considered prepaid expenses.

This arrangement would reduce my "salary" significantly - most
assuredly reducing the company's tax liability.  The implication of
his offer is that I will also save on my taxes by receiving part of my
compensation in the form of prepaid expenses.  I have limited
knowledge of taxes and loopholes but I believe the only way I would
gain anything from this is to accept the "expense" money and not
report the income.

The only way this would be any benefit is if it were legal for a
company to pick up the tab on some of my existing monthly expenses
like cell phone, disability insurance premiums, gasoline, internet
connection.

My question is - is it ever legal for an employee to accept monthly
expense money and not report it as income?

Hi member33,

Briefly, yes, and it is the preferred method of being reimbursed for
company expenses. Under the "Accountable Plan" reimbursed payments
paid to you are not considered wages and therefore are not taxable as
long as you "adequately account to your employer for these expenses
within a reasonable period of time". However, you will have to return
any over-payment. The following IRS website explains expense
reimbursements in detail.

IRS: Reimbursements:
"Reimbursements treated as paid under an accountable plan, as
explained next, are not reported as pay. Reimbursements treated as
paid under nonaccountable plans, as explained later, are reported as
pay."
Accountable Plans
"To be an accountable plan, your employer's reimbursement or allowance
arrangement must include all three of the following rules.
  1. Your expenses must have a business connection - that is, you must
have paid or incurred deductible expenses while performing services as
an employee of your employer.
   2. You must adequately account to your employer for these expenses
within a reasonable period of time.
   3. You must return any excess reimbursement or allowance within a
reasonable period of time."
Employee meets accountable plan rules:  
"If you meet the three rules for accountable plans, your employer
should not include any reimbursements in your income in box 1 of your
Form W-2. If your expenses equal your reimbursement, you do not
complete Form 2106. You have no deduction since your expenses and
reimbursement are equal."
Returning Excess Reimbursements:
"Under an accountable plan, you are required to return any excess
reimbursement or other expense allowances for your business expenses
to the person paying the reimbursement or allowance. Excess
reimbursement means any amount for which you did not adequately
account within a reasonable period of time. For example, if you
received a travel advance and you did not spend all the money on
business-related expenses, or you do not have proof of all your
expenses, you have an excess reimbursement."
http://www.irs.gov/publications/p463/ch06.html#d0e6672

Accountable plan or non-accountable plan:
"Make sure you ask your employer if your company is using an
accountable plan or a non-accountable plan. Reimbursed payments under
a non-accountable plan are treated as income and the employee can
claim deductions for business expenses. The accountable plan advances
employees or reimburses employees for travel expenses. Payments to
employees under the accountable plan are not included in the
employees' gross income and are not reported on a W-2 form.
http://www.cpa2client.com/DCv2/article.asp?key=tbsacpa&article=42

An Accountable Plan is the Best Plan:
"An accountable plan for reporting and reimbursing expenses is simple,
keeps employees from paying income tax on reimbursements and
constitutes good management. Keep public confidence and avoid the
excess-benefit tax with an easy-to-implement policy."
http://www.kdv.com/nonprofit-articles/exp_reim.html

I hope this helps to clear things up for you. If you have any
questions, please post a clarification request *before* closing/rating
my answer and I'll be happy to reply.

Thank you,
hummer

Google Search Terms Used:
Accountable plan irs

I was also able to use my own knowledge.

Very good answer and quick response.  Thank you.