Bilbao's transfer policy means that they are limited to signing Basque players.
Llorente will see his contract with Tottenham expire at the end of the season, and the 33-year-old has been strongly linked with a return to Spain.
Alkorta has said that Bilbao want to re-sign Llorente, who scored 118 times for the club between 2005 and 2013, while United midfielder Herrera is also a target.
The 29-year-old is also out of contract at the end of the 2018-19 campaign and despite being reinstated to United's starting XI under Ole Gunnar Solskjaer, his future is far from secure.
"We are interested in Javi Martinez, Ibai [Gomez], Ander Herrera, Llorente..." Alkorta told La Cadena Ser. "It's obvious that any player that can play for Athletic is of interest to us.
"Nothing is easy but we are interested in having all of the ones that can come. We have not made any moves yet. We will start on Tuesday and we will see what can be done."
Herrera turned out on 128 occasions for Bilbao between 2011 and 2014 before joining United. body check tags ::