Goddard is likely to join in full training this week, as the Bombers gear up for their NAB Challenge campaign.
"Brendon has had a very minor hamstring injury which he has recovered from very well," Bombers club doctor Brendan De Morton told essendonfc.com.au.
"He will be back into near full training either tomorrow or on Friday, depending on how he feels over the next few days."
Midfielder Jake Melksham (foot) is in doubt for the club's NAB Challenge opener clash against Gold Coast at Metricon Stadium on Monday night.
Melksham rolled his ankle at training on Monday, however the club is confident he will return to training later this week.
"Jake has had a problem with his foot which is an old injury which he occasionally rolls and jams it up a particular part of his foot," De Morton said.
"It caused him to look relatively bad when it happened yesterday but hopefully it will settle and we are quite optimistic that in a day or two he will be right."
Dyson Heppell, who has been dealing with back spasms, is available for selection in the game against the Suns.
Ruckman Tom Bellchambers, who was placed on the club's long-term injury list on Monday, is the club's only major injury.
