I think BA would buy if bmi were for sale, yes there would be anti trust issues that would mean releasing of slots and so on, bit in my view it's very unlikely anyway.
From LH point of view it has no pressing need to sell and whilst disposing of bmi would boost LH group profits only by removing the losses racked up by the bmi group,losses which are trending down after taking into account various one off events. The bmi group exposure to mid east and African markets is hurting at present but these routes offer tremendous upside opportunities when things settle down, London to Tripoli could be a gold mine in a years time.
The general view seems to be that bmi regional is marginally profitable baby marginally loss making with the bulk of group losses still coming out of bmi mainline,but its worth remembering that much of bmi heavy maintenance is done by LH tech now, baby 737 c check program alone will be over 10m Euro to LH
Like the baby Monarch rumour and the regional SN rumour I think this will come to nothing