Amin Elhassan breaks down the Rockets' chances of acquiring Iman Shumpert from the Cavaliers. (0:58)

The Houston Rockets covet Cleveland Cavaliers swingman Iman Shumpert and have engaged in talks with the Cavaliers about acquiring Shumpert before Thursday's trade deadline, according to league sources.

But the Cavaliers, sources say, would want Rockets guard Patrick Beverley as the primary return in a Shumpert trade. And Houston, sources said Wednesday, is resistant to parting with Beverley, who ranks as its top on-the-ball defender on the perimeter.

Sources say New York and Chicago have also expressed interest in Beverley, who wants to remain in Houston.

"At the end of the day I understand this is a business. I enjoy my time here with Houston," Beverley said before Rockets practice in New Orleans on Wednesday. "If anything does happen, I'll be fortunate and be happy to play back home [Chicago] and be happy to help an organization like the Knicks or an organization like the Cavs, if something does happen. But my loyalty is to Houston right now, and until that changes, that's where my loyalty will stay."

Shumpert is in his sixth season in the league, the first three with the Knicks. He came to Cleveland in the same deal that landed J.R. Smith with the Cavaliers. Shumpert has career averages of 7.4 points and 3.5 rebounds per game. In 51 games this season (15 starts), he is averaging 7.8 points and 2.9 rebounds.

Beverley has spent his five-year career with Houston. He is averaging 9.6 points, 5.6 rebounds and 4.4 assists this season.

‎ Iman Shumpert has started 15 games for the Cavaliers this season. David Liam Kyle/NBAE via Getty Images

Having significantly exceeded preseason expectations so far this season, led by MVP contender James Harden and new coach Mike D'Antoni, Houston is aggressively trying to strengthen its roster to cement itself as the foremost threat to the Golden State Warriors in the Western Conference.

The Rockets acquired high-scoring guard Lou Williams from the Lakers on Tuesday.

In addition to swingman Corey Brewer, whom Houston shipped to Los Angeles in the deal for Williams, Houston has been shopping guard K.J. McDaniels for weeks and, according to sources, would try to include McDaniels in any deal if talks with the Cavaliers progress.

Sources say the Cavaliers, meanwhile, have entertained the prospect of trading Shumpert at various points this season but have shown some hesitation given Smith's long-term injury absence.

Information from ESPN's Calvin Watkins contributed to this report.