The pair had been given extra time off after helping England to victory in the European Under-21 Championship earlier this month.
However, This Is Anfield understands they are scheduled to report back in the latter part of this week to start preparations for the new campaign.
The expectation is that both players will resume full training following Liverpool’s first pre-season friendly against Karlsruher on Wednesday.
And that could put them in contention for a behind-closed-doors meeting with Greuther Furth next Monday.
Jones will be out to be build on a strong showing in Georgia that saw him named in UEFA’s Team of the Tournament alongside five of his England teammates.
The Scouse midfielder also enjoyed an impressive end to last season at club level, carving out a regular starting spot after overcoming an injury-hit start to the campaign.
As for Elliott, he more often featured as a substitute for England at the Euros, but scored on his only start as he played a key role in his country’s success.
The 20-year-old made 46 appearances in all competitions for the Reds last term, scoring five goals.