teams that fire their coach have to satisfy the Rooney rule and interview some minority candidates. They also have to seek permission from SF to interview Harbaugh since he is under contract (otherwise it would be tampering). Now, in theory a team that is currently without a coach can seek permission to interview Harbaugh (Raiders) ASAP but Harbaugh himself can and likely has refused the opportunity to meet with them before the season is over.
In other words, unless it is Oakland there is almost no NFL team that will be able to get this done very quickly. The longer it drags out, the worse it is for UM. We will either know very quickly that it is Michigan (that did ask for and received permission to meet with Harbaugh) or we will hear what teams he wants to meet with in the NFL (if any). If it doesn't happen quickly (i.e. Monday or Tuesday) than I think UM is going to be SOL.