By Tova Cohen and Ari Rabinovitch

TEL AVIV, July 26 (Reuters) - After months of sparring in a hostile takeover bid for rival Mylan NV, Teva Pharmaceutical's move to buy Allergan Plc's generic drug business instead could be a smoother ride that will bring bigger returns, faster.

Israel-based Teva, the world's largest generic drugmaker, is in advanced talks to buy Allergan's generic drugs unit for between $40-45 billion dollars, according to a person familiar with the matter.

News of the deal broke on Saturday after Teva's $40 billion bid for Mylan hit a snag when a Dutch foundation linked to Mylan bought temporary control of half the company in an attempt to block the takeover.

A Teva spokesman declined to comment on possible talks with Allergan.

Though the Teva-Mylan feud has hogged the industry spotlight since April, Allergan' generics business may actually have been Teva's first choice. Teva CEO Erez Vigodman is believed to have approached Allergan last year, which was called Actavis prior to a March merger.

In June 2014, just a few months after joining the company himself, Vigodman hired the former head of Actavis' generic drug business, Sigurdur Olafsson, to fill a similar role at Teva.

"There was previously a preference for Actavis over Mylan but for some reason it didn't materialise," said Bank of Jerusalem analyst Jonathan Kreizman.

Should the deal with Dublin-based Allergan now go through, there will be two big upsides for Teva, he said.

First, there is less overlap than with Mylan. Teva has been planning a generic version of Mylan's EpiPen, a billion-dollar product, while Mylan has been working on a generic version of Teva's best-selling multiple sclerosis drug Copaxone.

In the short term, Teva would benefit from removing the uncertainty over the outcome of the Mylan deal that has weighed on its stock.

Since hitting a year high of $68.74 in New York on April 9, just before speculation on a possible Mylan bid had surfaced, Teva shares are down more than 10 percent, closing on Friday at $61.85.

Kreizman said he assumes the size of the deal would be similar in scope to Mylan, noting Allergan has about 8 percent of the U.S. drugs market, compared with 9 percent for Mylan and 14 percent for Teva.

"Assuming the entity is more or less the same size, valuation is less of an issue," he said.

The Mylan deal is hard for the market to digest, he said, while "any friendly transaction ... would have better impact."

Allergan's generics operations has about $7 billion in sales, said Umer Raffat, an analyst with investment research firm ISI Group.

"Theoretically, a Teva/Allergan generics business combo offers Teva the opportunity to get what it was looking for without having to go through Dutch courts," he said.

This includes boosting its scale and getting access to complex generics like injectables as well as biosimilar drugs through Allergan's partnership with Amgen on oncology biologic drugs, he said.

(Editing by William Hardy)