The Nets have been discussing the move internally for some time and, according to one source, are "comfortable" with where the Lithuanian big man is medically after back issues scuttled the Houston Rockets' trade of Motiejunas to Detroit in February.
No deal with Motiejunas is expected to happen before Friday, sources said, with Brooklyn playing host to the Milwaukee Bucks on Thursday night.
If the Nets indeed go through with their plans to sign Motiejunas, Houston would then have three days to match any offer.
Houston pulled its most recent offer to Motiejunas last Tuesday, when the sides couldn't come to terms on a deal before the Rockets' self-imposed Nov. 22 deadline.
The Nets have nearly $19 million in available salary-cap space to assemble an offer that will be unpalatable for Houston to match. Brooklyn, though, was foiled twice in restricted free agency over the summer, seeing its hefty offer sheets to Miami's Tyler Johnson (four years, $50 million) and Portland's Allen Crabbe (four years, $75 million) matched by those teams.
Nov. 23 was the last day that players could be signed this season and remain eligible to be dealt on the league's annual trade-deadline day, which falls on Feb. 23. ESPN reported in early November that the Rockets, as a result, picked that date as their own internal deadline to sign Motiejunas, fearing his value would decrease if they didn't have the ability to trade him.
Sources told ESPN on Nov. 4 that the Rockets were offering a two-year deal starting in the $7 million range, but with only the first season fully guaranteed for the 7-foot, 223-pounder.
ESPN reported last week that Motiejunas was "surprised and upset" that negotiations with the Rockets had dragged on so long. Motiejunas' camp has been trying to drum up interest in his client from the handful of teams around the league that possess the cap space to present a representative offer sheet and appears to have found a willing suitor in Brooklyn.
Motiejunas could have made himself an unrestricted free agent next summer had he been willing to play out this season on Houston's $4.4 million qualifying offer, but he let the qualifier expire Oct. 1, hopeful that a long-term deal would eventually materialize.
The Rockets have been unwilling to guarantee more than the first year of a multiyear deal in a nod to the 26-year-old's injury history. Houston traded Motiejunas to Detroit in February, only for the Pistons to void the deal and send him back to the Rockets because of a failed physical stemming from Motiejunas' back troubles.
ESPN Staff Writer Calvin Watkins and The Undefeated's Marc J. Spears contributed to this report.