Murray, beaten in this year's Australian Open final by Novak Djokovic, is keen to add some depth to his support crew as his coach Amelie Mauresmo has other commitments, including being captain of France's Fed Cup team.
"I'm super excited and I'm really looking forward to join @andy-murray and his team for a test week," Bjorkman, 42, said on his Twitter feed.
Bjorkman, a former Wimbledon semi-finalist who also excelled as a doubles specialist with nine grand slam titles, is currently appearing in Sweden's Let's Dance TV show so it is unclear when his trial week with Briton Murray would take place.
World number five Murray, twice a grand slam champion, trimmed his entourage at the end of last season with hitting partner Dani Vallverdu jettisoned.
However, since reaching the final in Melbourne, the Scot has suffered some disappointing defeats, losing to Gilles Simon in Rotterdam after beating the Frenchman 12 times in a row and then falling to Croatian teenager Borna Coric in Dubai.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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