Cole was a notable absentee from a civic reception in the city on Thursday night, with Football Association claims the Chelsea defender was "resting" sparking fears of a potential injury.
However, Cole felt fit enough to train this morning, although it was expected to be a light session.
Indeed, all 22 members of the England squad - Jermain Defoe remains in England following the death of his father - were present for the session which took place in front of 3,000 invited guests.
Later, the England squad were going to split, with six members, including Wayne Rooney and Joe Hart, due to travel to Auschwitz along with manager Roy Hodgson and FA chairman David Bernstein, with the remainder set for a tour of Oskar Schindler's factory, reinforcing England's commitment to the local area.
The policy is in marked contrast to their stay at the World Cup in South Africa two years ago when England were criticised for adopting an isolationist approach when their training camp and hotel were both at the same remote location in Rustenburg.
The Chelsea Originals T-shirt from adidas. The classic look of the trefoil can't be beat.
$44.99
Perfect for carrying your soccer gear to the game or to use to go to work or school. Go Chelsea.
$69.99
Petr Cech will be wearing this NEW Keeper jersey in the 2013/14 Premier League campaign. Be bold.
$99.99
The latest craze in caps is the old school trucker cap. Get you Chelsea Trucker cap today and be on trend.
$14.99
The Chelsea badge poster is a great addition to any fans room. Show you bleed blue.
$9.99
Check out the Chelsea 1976 Retro Soccer jersey. Wear these classic looks when you go out.
$59.99
The 2013/14 Chelsea replica soccer jersey. The sure sign you are a fan of the Blues is by wearing the official jersey.
$89.99
Get your young Chelsea fan started early with this Chelsea Mini Kit.
$54.99
The 2013/14 Chelsea long sleeve soccer jersey. The best fans have a long sleeve jersey.
Pull on a more traditional look with the Chelsea Team Polo. Simple but classic.
$37.99