Allen had previously also been linked with the Cowboys.
Former Minnesota Vikings defensive end Jared Allen is understood to be set to visit the Seattle Seahawks for a second time ahead of a possible deal being reached.
With the Dallas Cowboys now seemingly out of the race after signing former Chicago Bears star Henry Melton, the defending Super Bowl champions have emerged as the favourites to land the 31-year-old.
According to ESPN, Allen will make a second trip to visit the Seahawks after making an initial journey for talks on Sunday before making his way to Dallas.
The defensive end has insisted throughout free agency that he is looking for a team that has “a chance to win”, whilst also looking for a fair contract, and it would appear that Seattle fulfil the first part at least.
It remains to be seen whether or not the two parties are able to agree on terms, although speculation suggests that Allen is vaguely aware of what is being offered and is interested which has resulted in the second meeting being arranged.
The Seahawks had already re-signed defensive end Michael Bennett before the free agency market even opened, while Cliff Avril is under contract for another season too.
As a result it is likely that Allen will fill the role left behind by Chris Clemons, although Seattle will have to tread carefully in terms of what they offer him with key decisions to be made in the coming year.
Both Earl Thomas and Richard Sherman will be expecting contract extensions next summer while quarterback Russell Wilson will also be eligible for a new deal after next season which will all require significant cap space to operate within.