As the Mets sharpen their focus on trading for offensive help as well as a late-inning relief pitcher, they continue to push for the Brewers’ Jonathan Lucroy and the Angels’ Joe Smith, sources said Friday.

With a handful of contenders vying for Lucroy, the righthanded-hitting catcher/first baseman, the Brewers could push the bidding right up until Monday’s 4 p.m. nonwaiver deadline, just as the Tigers waited before sending Yoenis Cespedes to the Mets a year ago for Michael Fulmer, their top pitching prospect.

Entering Friday night, Lucroy, 30, was batting .300 with 13 home runs and an .848 OPS. He also is relatively inexpensive, with less than $2 million left this season and a $5.25-million option for 2017.

The Mets are not on Lucroy’s limited no-trade list, according to ESPN. That group reportedly includes the Twins, Angels, A’s, Padres, Mariners, Nationals, Indians and Tigers. While that could make it easier for the defending National League champs to strike a deal, the cost could be prohibitive, and it is unclear if the Mets would be willing to part with a top prospect such as Amed Rosario or Michael Conforto to include in a package with Travis d’Arnaud, who seems to be a must-have in any Lucroy swap with the Brewers.

Recently, a club official insisted that “Rosario is going nowhere” in a trade. And in the days leading up to the deadline, the Mets have fielded calls on Conforto, though they haven’t entertained any of those proposals.

Dominic Smith, another top prospect, also might garner attention from rival clubs. But several talent evaluators insisted that he is regarded as being a tier below the likes of Rosario and doubted that he’d be valuable enough to make a Lucroy deal a reality.

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With Friday’s announcement that Juan Lagares is out six weeks because of thumb surgery, along with Cespedes’ lingering leg issues, the Mets have to determine just how badly they need offensive help. Heading into Friday’s game against the Rockies, they were hitting .204 with runners in scoring position, rock bottom in the majors and far below the next-worst Yankees, who were at .220.

The Mets also rekindled past discussions with the Reds about Jay Bruce, a slugger they were interested in a year ago before the Cespedes trade. Despite conversations between the two clubs, however, a source suggested Friday that it is not a good fit and that a deal is unlikely.

The Mets also had internally discussed the A’s Danny Valencia at one point but apparently will not target him for infield help in the days leading up the deadline, even with his slash line of .299/.351/.461 and 13 home runs.

The Mets were in the market for relief help long before Jeurys Familia blew back-to-back save chances this week after converting 52 straight in the regular season. Familia is part of a formidable trio with setup man Addison Reed and Hansel Robles, but with concerns about overuse, discussions have been ramped up with the Angels regarding Smith, who began his career with the Mets in 2007. The sidearming righthander, 32, entered Friday with a 3.96 ERA in 37 appearances this season and had not allowed a run in his last seven outings.

The pursuit of Smith seems to reinforce that the Mets are not willing to pay a premium for closer types — they did not ask the Angels about Huston Street — and are targeting more middle-tier relievers such as Smith, with an expiring contract that has roughly $1.8 million left for this season.

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Beyond that, the Mets could always look to expand on their pitch for Lucroy by asking the Brewers to include a reliever such as closer Will Smith or Jeremy Jeffress, a proposal that would force them to ante up with more minor-league talent in return.