Saul has been preparing to leave Atletico Madrid all summer and the Spanish champions are also keen to let him go.
But the speculation over his future has only come to head towards the final days of the transfer window.
Chelsea have tabled a bid to sign him on loan with an option to buy, and Manchester United are also interested.
It has been claimed that the Red Devils are trying to play safe with their interest in the 26-year-old midfielder.
Ole Gunnar Solskjaer wants to bring in a midfielder before the end of the transfer window, but lack of sales has hampered Manchester United’s chances of signing one more player after Jadon Sancho and Raphael Varane.
The Premier League giants are prepared to do business though if the up-front cost of signing a player can be kept in check.
With Atletico Madrid open to loaning him out initially, Manchester United are exploring signing Saul before Tuesday’s transfer deadline.
More funds could become available if a player such as Jesse Lingard is sold towards the end of the transfer window.