Pepe left Besiktas staff a cash tip as a parting gesture after agreeing to terminate his contract with the Turkish club, sources have told ESPN FC.
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The Istanbul-based outfit are desperate to sign a striker over the transfer window and the Mexico star is among the players being targeted.
Reports in Turkey had claimed Besiktas wanted to terminate Loris Karius' loan, but ESPN sources have confirmed this is not the case.
Real Madrid go into Sunday's Clasico at Barcelona with Julen Lopetegui under increasing pressure.
Liverpool keeper Loris Karius, on loan at Beiktas, was beaten by a deflected cross against Malmo and faced heavy criticism on social media.
Loris Karius said it took him nearly two weeks to get over the Champions League final defeat and that he was never told he had to leave Liverpool.
Portugal defender Pepe said he was thrilled to be able to score after winning his 100th cap in the 1-1 draw against Croatia on Thursday.
On-loan Liverpool goalkeeper Loris Karius conceded a late equaliser in his first appearance for Besikstas, a 1-1 draw against Bursaspor on Sunday.
The German was unveiled as a Besiktas player on Wednesday, having joined the Turkish side on a two-year loan deal that could become permanent.
Besiktas have completed the signing Loris Karius on a two-year loan, Liverpool confirmed on Saturday.
Fulham have signed Spanish goalkeeeper Fabricio Agosto Ramirez "Fabri" from Turkish side Besiktas on a three-year contract.
First-choice Besiktas goalkeeper Fabri Agosto Ramirez confirmed he's set to join Premier League side Fulham.
Besiktas are considering a move for Arsenal goalkeeper David Ospina following an offer from Fulham for their No. 1 Fabri, sources have told ESPN FC.
Former Madrid player Guti was reportedly considered as a candidate to fill the vacancy left by Zinedine Zidane's resignation as coach.
Benfica forward Anderson Talisca has opted to join Chinese Super League club Guangzhou Evergrande on a six-month loan following links to Man United.
The fixture was initially abandoned after Besiktas boss Senol Gunes was struck in the head by a foreign object.
Besiktas have refused to play the rescheduled final 33 minutes of their Turkish Cup semifinal against Fenerbahce.
Fenerbahce and Besiktas will complete the remaining 33 minutes of their abandoned Turkish Cup semi-final clash next Thursday.
The Istanbul derby was abandoned at Fenerbahce on Thursday after Besiktas manager Senol Gunes sustained a head injury from a thrown object.
The ginger cat ventured onto the playing area during the second half, with referee Michael Oliver halting the game until it had gone.
Bayern Munich and Besiktas were just playing out the string in their lopsided Champions League match on Wednesday when a cat took over.
Bayern Munich eased into the Champions League quarterfinals 8-1 on aggregate after a 3-1 victory at Besiktas in their round-of-16 second-leg tie.
Having no fixed starting XI led to Bayern struggling before the second half domination of Besiktas. It may hurt them in games to come.