A club spokesman said: "Our coaching staff are taking a look at Anthony for the next few days.
Basso's agent Tommaso Angelini has already spoken to the Edinburgh side and expects a permanent deal to be done in the coming weeks.
"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."