The French forward has been offered a three-year deal by Cluj boss Mircea Rednic and is keen to try something new after seven years in Scotland.
Tade moved to McDiarmid Park from Inverness last summer on a one-year contract but still has the option of an extra year in Perth.
However, Press Association Sport understands he has his heart set on a fresh challenge.
Saints boss Tommy Wright, however, has criticised the player after claiming Tade had informed the club he planned to sign on again.
Wright told Press Association Sport: "We've heard that Gregory is on his way to Romania but we haven't had anything confirmed yet. If he does go it will be disappointing because he told us he would be re-signing. We were waiting for him to come in last week and sign his contract and he didn't do it.
"We didn't think we needed a striker but at this stage in the summer we now find (we) may have to go out and find one. We'll deal with that but we were told he was going to take up the option and to learn that might not be the case at this late stage is disappointing."
The 26-year-old first moved to Scotland in 2006 when he signed for Forfar. Spells at Stranraer, Clyde and Raith Rovers followed before he won his move to the Scottish Premier League in the summer of 2011 with Inverness.
The lure of Europa League football convinced him to switch to St Johnstone a year later and he struck his first goal on his debut for the club in their Europa League qualifier draw with Turkish side Eskisehirspor last July, before finishing the season with six goals from 41 outings.
Cluj have won the Romanian title three times since 2008 but ended last season's Liga I Bergenbier campaign in ninth place.