According to "Lives of the queens of England, from the Norman conquest." by Agnes Strickland and Elizabeth Strickland in 1842, Mary had given her consent to the marriage to Dom Luis.
Apparently, the condition that Luis and Charles V wanted from Henry VIII was the revocation of Mary's status as illegitimate, and they were willing to waive her rights in the line of succession. Early in 1536 Henry VIII rejected this, but by the end of the year he was willing to agree to this. At the same time Francis I was proposing an alliance with a marriage between Mary and the Charles Duke of Angoulême. The French too demanded that Mary be legitimised as well, so Henry realised that this would be a pre-condition to marrying Mary to any foreign prince.
The negotiations between Henry VIII and Charles V in early 1538 were the most intense as Charles V pushed Christina to marry Henry and wanted an alliance with England. Charles was willing to not only give Milan to Luis, but also push for a general council of the Church to reform the papacy and allow the divorce from Catherine of Aragon to be recognised. In February 1538 the diplomatic fury between Hampton Court and Brussels seemed to be at its greatest. By March it seems that the marriage was assured, and only an offer by Francis I to marry Henri, Duke of Orléans (future Henri II) made the negotiations drag on.
It does seem that Francis I was particularly anxious about Henry VIII marrying Christina of Denmark, with the possibility Henry VIII claiming the Duchy of Milan for himself. In May 1538, Henry VIII withdrew from the plans to marry his daughter to the Duke of Beja, and looked towards the French. However, in October 1538, Charles V agreed that if Mary should ever succeed to the crown of England, Luis would abide by the laws of England.
What did in effect happen during the second half of 1538 though was that peace between France and the Habsburgs ensued, and Henry VIII lost his opportunity. The first truce between the continental powers in June 1538, was followed by a meeting between Francis I and Charles V mediated by Pope Paul III the following month. This made Henry VIII fearful of an alliance between France and the Habsburgs against him. The excommunication of Henry VIII by the pope in December 1538 (though this could have been avoided through the marriage) seems to have further intensified his fears. As a result, the marriage offers stopped coming to Henry and he increasingly became paranoid of not having enough heirs. This was coupled with the rebuff of Marie de Guise and her marriage to James V of Scotland instead, making Henry feel encircled.