As said by others above, sending a ready message (REA) indicated that the aircraft is ready to pushback without delay. Each airport has a set taxi-time registered with CFMU, which is the time that the aircraft is expected to take to taxi from the stand to the runway. CFMU takes the ready message and, in the best case scenario, adds the taxi time to the time the ready message is filed and makes that the new CTOT (slot).
There is an option to specify a new taxi-time in the ready meassage (called the MINLINEUP time) which allows ATC to extend the taxi-time. I think the scenario described is suitable for the use of a MINLINEUP, but I suspect some ATC units will be sceptical and won't send the REA until the tug is attached.
It is worth having a look at the CFMU ATFCM User Manual (available as a
PDF from Eurocontrol) which contains the relevant procedure in section 4.3.3.4.