The group, which also owns the Premier Inns budget hotel chain and restaurants Beefeater and Brewers Fayre, has been relatively unaffected by the financial meltdown due to the strength of its brands in the value for money sector.
Parker, who unveils Whitbread's interim results on Tuesday, should announce a healthy six months for the leisure group. But analysts say that Costa Coffee, which is performing well, could be offloaded. In the past few years the group has moved to slim down its business, having sold Marriott, Deep Pan Pizza, TGI Friday and David Lloyd.
Whitbread has already merged its Premier Inn hotels, Beefeater restaurants and Brewers Fayre pubs into one business in a bid to save 25 million a year, and analysts say Costa now looks "out on a limb".
Nomura analyst Simon Larkin said: "We would not discount the group potentially disposing of Costa Coffee when the time is right, or pub restaurants, and we could also envisage a scenario where owned real estate is used as a source of future funds for budget hotel expansion."
Another City analyst said: "Whitbread has effectively put the hotels and pub divisions together, so it does leave Costa looking a little bit of an afterthought."
A month ago the company hailed an "outstanding performance" at Costa Coffee as it flagged up half-year numbers at the top end of market hopes.
Although underlying pre-tax profits are likely to come in around 7 per cent down on last year at 113m, this represents a creditable showing in a year of recession. The firm also managed to reclaim its spot in the FTSE 100 Index in September after losing its blue-chip status in June.
Although Premier Inns' sales fell 7.7 per cent on a year earlier in the 24 weeks to August, dragging group like-for-like sales 2.6 per cent lower, Costa rose 2.7 per cent and added 88 new outlets.
Meanwhile, the company's pub restaurant brands – Beefeater, Brewers Fayre, Table Table and Taybarns – grew comparable sales by 2.1 per cent and continued to gain market share.