Taveres worked under Jol at Hamburg and also had a stint in England while on loan at Middlesbrough during the 2010/11 season.
With injury concerns mounting and a disappointing transfer deadline day, Fulham have been keen to boost numbers in the centre of the park, even with the introduction of Greek international Giorgos Karagounis.
This led to much speculation about the futures of free agents Owen Hargreaves, Nigel Reo-Coker and Thomas Hitzelsperger but, last week, Jol claimed he was looking at a particular player from abroad who he had managed before.
Taveres was clearly that man and the Fulham boss expects all loose ends to be tied up very soon.
"Hopefully in an hour or so we will have a deal with him," Jol said on Friday afternoon.
"It is almost a done deal because I had seven midfield players when I came and I now have only two.
"Tavares is a back-up player for me on a short-term contract."