Jared Allen was accompanied on his second visit to the Seattle Seahawks by his wife, family members and his agent. But any sense they were brought together presuming an introductory news conference disintegrated when they left Seahawks headquarters and returned to their family offseason home in Arizona without finalizing a contract or otherwise committing to join the defending Super Bowl champions.

In a text message later Thursday, Allen said, "We are heading home and will consider their offer and I'll make my decision this weekend."

Earlier, league sources described the Seahawks and Allen as working on the final details of a contract that -- barring unforeseen developments -- would be signed as soon as Thursday.

Ken Harris, who represents Allen, indicated the player had more than just Seattle's offer to deliberate before making a commitment. The only other team Allen is known to have visited was the Dallas Cowboys, who signed defensive tackle Henry Melton earlier this week. Sources indicated that the Cowboys were not interested in also signing Allen unless he lowered his contract demands.

Among the likely challenges for Seahawks general manager John Schneider and coach Pete Carroll was convincing Allen to accept being a prominent situational player in Seattle's defensive line rotation, one that was pivotal to the team dominating Peyton Manning and the Broncos in their Super Bowl victory in February. The Seahawks led the NFL in fewest points and yards allowed this past season, and created the most turnovers in the league -- a feat previously accomplished by the 1985 Chicago Bears.

Jared Allen has 128.5 sacks in 10 seasons, including 85.5 over the past six seasons with the Vikings. Brace Hemmelgarn/USA TODAY Sports

Allen has 128.5 career sacks, 12th most in NFL history. He has seven consecutive double-digit sack seasons, including 11.5 last season in Minnesota, but his contract offers seemed likely to be for significantly less than DeMarcus Ware and Julius Peppers got for changing teams in free agency.

The Broncos signed Ware for three years and $30 million, with $20 million guaranteed. Peppers accepted a three-year deal totaling $30 million maximum, $7.5 million of which is guaranteed.

Allen has in mind what he considers his "walk-away" price -- his bottom-line number for continuing to play rather than retiring.

The Seahawks' first offseason priority was achieved when the team signed defensive end Michael Bennett to prevent him from becoming an unrestricted free agent. They then released defensive end Chris Clemons. The Seahawks' deep rotation in the defensive line was important to maintain, especially since the team lost some coverage with cornerbacks Brandon Browner and Walter Thurmond defecting in free agency.

They have $15.2 million in salary-cap space but have been conservative in free agency because they will be pursuing long-term deals with quarterback Russell Wilson, Earl Thomas and Richard Sherman within the next 12 months.

ESPN.com Vikings reporter Ben Goessling contributed to this report.