England coach Duncan Fletcher wants to make sure the majority of his leading players are well-rested before the first Test against Sri Lanka on May 11 at Lord's, which marks the start of another busy home international programme.
But left-handed opening batsman Trescothick, who returned to England before the recent India Test series started with what he said this month was a "virus", was selected for Somerset's county championship opener against Gloucestershire starting Tuesday.
And fast bowler Jones, who has not played for England since the fourth Ashes Test against Australia at Trent Bridge last year following a knee injury, hopes to take the field for Glamorgan's match against Cardiff University Centre of Cricket Excellence on Wednesday.
"If I want to get back into England side I've got to get some wickets and prove my fitness and hopefully that's what I'm going to do this week and next week," said Jones.
"It's an exciting time for me, it's been a long and frustrating winter and I'm just looking forward to getting back on the field," the Welsh quick, son of former Test paceman Jeff, also told the BBC.
Key all-rounder Andrew Flintoff, who added captaincy to his already heavy workload during the tour of India, following the departures of vice-captain Trescothick and Vaughan, is set to play just a solitary one-day match for Lancashire before the three-Test series against the Lankans gets underway.
However, spinners Shaun Udal (Hampshire) and Monty Panesar (Northamptonshire), who didn't feature in the one-day series in India, are both free to play for their counties without restriction.
Meanwhile it is uncertain when England captain Michael Vaughan (knee), fast bowler Stephen Harmison (shin) and left-arm spinner Ashley Giles (hip) will return from their injury problems.