Hearts hope to re-sign Czech Republic winger Rudi Skacel by the beginning of next week.
The 31-year-old has been training with the Edinburgh club despite being out of contract since last season.
And manager Jim Jefferies said: "He's back training with us, but he's not quite 100% ready for matches just yet.
"He has contract talks going on with the club and they'll hopefully be resolved tomorrow or certainly over the weekend."
Skacel joined Hearts on loan from Panathinaikos in 2005 before heading for Southampton on a permanent deal.
Following a loan spell with Hertha Berlin and permanent moves to Slavia Prague and Larissa, he returned to Hearts in September.
Now he could extend his stay at the Edinburgh club despite failing to travel to Germany with his team-mates last week as he is further behind in his fitness following the Achilles problem that ended his season prematurely.
However, Jefferies revealed that the winger could play his first pre-season match when Royal Antwerp visit Tynecastle on Sunday.