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I am wondering if the asset price with dividend can be the numeraire?or generally, what can be a numeraire? any tradable asset price?

Generally speaking, a numeraire may be any positive non-paying-dividend asset.

if you want to use an asset providing income as numeraire, you have to consider the value of the asset with dividends reinvested. Think of the usual continuous interest money market account numeraire; this is effectively a risk free asset providing an income at a rate r. you can extend the same principle to risky assets.the numeraire does have to remain positive in value; to construct the risk-neutral measure wrt a particular numeraire N you need the relative asset prices S/N to be martingales, and if N goes to zero with positive probability then S/N goes to infty and so is not integrable.you don't have to choose an actual asset as numeraire; it can be a portfolio of assets which can change over time if you like. You can think of any such trading strategy as a kind of an asset anyway; imagine buying a fund that promised to follow that strategy; this is then an 'asset'. An example of when such a 'dynamic numeraire' might be useful is in the Libor market model, where the assets are a finite number of discount bonds, and one choice of numeraire is the trading strategy that holds the first discount bond until expiry, and then reinvests the proceeds into the second discount bond, and so on.