A GENERAL offer for shares in textile manufacturer Unisouth Holdings may be made, according to a company statement issued yesterday. ''The controlling shareholders of Unisouth have been contacted by a number of independent third parties which are presently formulating proposals concerning Unisouth which may result in an acquisition of shares in Unisouth, giving rise to an obligation to make a general offer,'' the statement said. But no firm intention to make an offer had been notified to the board, it said. Neither the proposals nor a general offer will definitely take place. The company urged shareholders to exercise extreme caution in dealing in the group's shares, which have recently risen in price and trading volume.