The 27-year-old is on loan at the Blues this season, and has started to show improvement in the last month.
According to the Daily Star, Chelsea have been impressed by Saul recently, and may even consider making his signing permanent in the summer.
The Blues had initially given up on Saul, but the player has now learned English and is performing much better.
His integration into the group has also improved, which managed Thomas Tuchel acknowledged recently.
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