Jenkins started all three Tests for the 2009 Lions, having done the same when Britain and Ireland's elite travelled to New Zealand four years earlier.
The star loosehead is in line to return to the starting XV for this Saturday's Six Nations encounter with Scotland.
Jenkins sat out the 30-17 defeat to England at Twickenham after picking up a calf injury in training.
His presence was missed by the 2005 and 2008 Grand Slam winners as they failed to beat the old enemy for the first time in four attempts.
"Gethin is doing well," said Wales physio Mark Davies.
"We are progressing his training this week, with a view to him taking a full part in Thursday's session."
If Jenkins is passed fit for the Millennium Stadium clash with the Scots, he is likely to replace Paul James of the Ospreys in the No1 shirt, with Saracens newcomer Rhys Gil the man expected to drop out of the matchday 22.