The Lawn Tennis Association has announced two new Challenger tournaments '“ one at the Scotstoun Tennis Centre in Glasgow starting on 28 April and the other at Loughborough University the following month.
Former World No 1 Murray's recovery from surgery in January is going well, better than expected, in fact.
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He is working hard on his strength and fitness in the gym and he hopes to be back on the practice courts in a week or two.
From there, it will be a case of increasing the intensity of his training and seeing how well he and his hip cope.
Murray, who has been overtaken as British No 1 by Kyle Edmund during his injury lay-off, had said he was hoping to be back for the grass-court season.
However, his management company later hinted he might be back before then and the firm and the LTA have been in contact.
A Challenger tournament is below the level of a main tour event and it would be a major coup for the LTA if the two-time Wimbledon champion entered.
Murray, though, is wary of setting deadlines. He has not played a competitive match since July and he has had two abortive attempts at a comeback, at the US Open in August and the Brisbane International at the start of the year.
He was devastated when he had to admit that his hip was nowhere near strong enough to withstand matchplay and will now only return when he is good and ready.
However, the fact that both Glasgow and Loughborough will be on indoor hard courts would be a significant factor.
Other, bigger, Challengers at the same time are on clay. For Murray, the switch from hard court to a grass court is relatively straightforward compared to the move from clay to grass.
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