The Gunners were unable to agree a deal for the centre-back earlier in the summer and reports have linked them to the Swans' talismanic attacking midfielder after Liverpool held firm on previous target Luis Suarez.
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"Nothing has changed," the Swans chief told the press. "There has been no contact, as far as our football club is concerned, in connection with anybody and we wouldn't welcome any bids.
"The overriding point from our football club is that we are not looking to sell any of our players and they are not up for sale.
"We want to strengthen our squad, we feel we've done that and we continue to look forward to the season ahead. That has not changed."
Reports have claimed that Swansea are tracking Wolves striker Kevin Doyle as they look to add depth up front, with Jenkins saying of the interest: "We are still looking for the right one and we will wait to see what develops."