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But the news is not so good for fellow Canterbury stars Johnathan Thurston and Sonny-Bill Williams who are not expected back until as late as mid-July.
Anasta is back to full training after suffering a rib cartilage injury two weeks ago and is tipped to run on against Canberra at Express Advocate Stadium in round 15.
Bulldogs teammate Glen Hughes is also expected back next week after enduring a spate of injuries.
However, Thurston (knee), who was expected to be fit this week, and Williams (ankle) - who was pencilled in for next round - have been told that they would not be fully fit until "early to mid-July".
"Johnathan Thurston and Sonny-Bill Williams are both making steady progress and are expected back sometime in early to mid-July," a team spokesman said.
Meanwhile, Wests Tigers lock Scott Sattler has succumbed to a hamstring tear and is out for "at least a week" after going down at training this week along with teammate Nick Graham (ankle).
Graham will miss the Tigers' "home" clash at Christchurch on Sunday against NZ Warriors along with Mark O'Neill (broken nose).
Lock Ben Kennedy (hamstring) has again succumbed to injury before Newcastle's clash against North Queensland at Townsville on Saturday night with his place in the 17-man side to be taken by either Kevin Henderson or Michael Young.
Fullback Robbie O'Davis is the likely Knights captain.
Cowboys pair Travis Norton (knee) and Ty Williams (thigh) are expected to play but inspirational lock Glenn Morrison is unlikely to run on again this season after injuring his back last weekend.
Souths could have prop Paul Stringer (back) back sooner rather than later after he was expected to be a last minute Premier League bench inclusion this weekend.
Rabbitohs skipper Bryan Fletcher won't be back for another "six to eight weeks"
Souths' Scott Geddes (pectoral tear) - who hasn't played NRL this year - was named as 18th man for the NRL clash against Melbourne on Saturday night - but looks like he will be dropped to Premier League.
Souths host a Melbourne outfit still sweating on veteran winger Matt Geyer (shin gash) who has a fitness test on Saturday.
Storm utility Andrew McFadden (ankle) is expected back in "a couple of weeks".
For Manly, Shayne Dunley is out with a sternum injury but teammates Sam Harris (back) and Chad Randall (knee/hamstring) have been cleared for the Sea Eagles' clash at Parramatta on Sunday.