Celtic manager Martin O'Neill will decide over the next few days whether to further his interest in Portuguese star Dani and Spanish international Ivan de la Pena.
The duo have been invited to Parkhead to have a look at the set-up and, having trained today, where the management began assessing the players' fitness.
The biggest concern is that neither player would be available for the first Champions League group stages and would therefore only be able to play in the club's domestic fixtures.
O'Neill said: "They are here at the minute on a fitness assessment and it is a chance for them to take a look at us and for us to have a look at them, nothing more than that.
"Obviously the big disadvantage is that neither Dani or De la Pena would be eligible to play in the Champions League and that is something that we would have to take into consideration.
"Things were very congested before the transfer window closed and it was relatively later on before we were made aware of the availability of both players," added O'Neill.
"It left us very little time to work with especially because neither party had any dealings with the other beforehand.
Both players are currently out of contract which would allow them to sign for Celtic despite the fact the transfer window has closed.
Midfielder De la Pena, who was nicknamed `the Little Buddha' when he broke through the ranks at Barcelona, has left Lazio.
But he is in his prime at just 26 years old while Dani is the same age and ready for a fresh challenge after being released by Atletico Madrid when his contract expired this summer.
Dani, who scored against Rangers in the Champions League during his time at Ajax in 1996, is an attacking midfielder who is capable of adding some spice to Celtic's squad.