A club spokesman said: "Our coaching staff are taking a look at Anthony for the next few days.
"Since Craig Gordon left the club there's clearly been a need to bring someone in, so Anthony will have the opportunity to get to know us, and us him."
Basso's agent Tommaso Angelini has already spoken to the Edinburgh side and expects a permanent deal to be done in the coming weeks.
"There is no doubt Anthony is a quality goalkeeper," said Angelini. "Roy Hodgson signed him twice when he was a manager in Norway with Viking Stavanger and in Italy with Udinese.
"Anthony was voted the best goalkeeper in the Norwegian top-flight in his time at Viking. He is in Edinburgh to look at the club and they, in turn, will have a look at him. He is keen to try Scottish football."