MEL GIBSON may be preparing to attempt to get full custody of his 4-year-old daughter with ex-lover Oksana Grigorieva, which could put the former couple in a bitter tug-of-war over little Lucia.

While the two cur­rently split custody of the girl, sources say Mel, 58, is con­sidering obtaining a “custody assess­ment” from family court because he believes he’s a better influence than Oksana and wants to have Lucia with him full time.

“It’s complete nonsense,” fumed one source. “Lucia means every­thing to Oksana and they have an incredibly close bond.

“Oksana is dumbfounded that he would even consider the idea of trying to gain more custody of Lu­cia. It shows how cruel he can be.

“In fact, she and some of her friends think that it would be nothing more than a clear demon­stration of spite on Mel’s part.”

In August 2011, the Russian singer, 44, reluctantly agreed to the 50/50 custody agreement after ini­tially declining a $15 million payout  from the “Mad Max” star. She even­tually got $750,000 spread out over several years, But now she is also said to be having second thoughts about the custody arrangement, partly because she may be con­cerned about Mel’s increasing commitment to his new love, says the source.

As The ENQUIRER recently re­ported, Mel has been dating Italian singer/songwriter Nadia Lanfran­coni since 2012 and insiders say she has a “remarkably soothing and calming influence over him.”

Added one insider: “His violent outbursts appear to be a thing of the past, at least when he’s around Nadia. What this really comes down to is that Oksana can’t bear the thought of Nadia winning over her daughter’s heart.

“She’s willing to do whatever it takes to stop Mel dead in his tracks.”