Lage, who worked under Carlos Carvalhal at Wednesday and Swansea, returned to his native Portugal last summer to coach Benfica's second string.
But after Rui Vitoria's departure by mutual consent as the start of this month, the 42-year-old found himself sworn in as caretaker boss and went on to win both of his matches in temporary charge.
Speaking via the club's official website on Monday, the Benfica president, Luis Filipe Vieira, insisted that despite rumours of a return to Lisbon for Jose Mourinho, he has not been in touch with any other coach, or agent, in the meantime.
"The story today, the present, is to tell you that the first option of Sport Lisboa e Benfica is Bruno Lage," he added. "It was well thought out, he is a man that knows our club very well, he knows what Benfica is, he knows the whole Club youth, he knows perfectly well all the goals that the Club has."
It is understood that another of Carvalhal's Sheffield Wednesday and Swansea backroom team, Jhony Conceicao, will step up alongside Lage.
Carvalhal, meanwhile, looks set to remain out of work as Nottingham Forest close in on Martin O'Neill's appointment, according to the BBC.
Should Sheffield Wednesday and Swansea have considered Lage for their recent managerial vacancies?
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