They are interested in keeping up to date with what you are doing
= ils expriment l'intéret de rester à jour avec ce que vous faites

It depends a bit on the context and register: who are 'you' and 'they', and in what context is this being said? Also, does it imply a positive action on 'their' part (they are going to keep an eye on 'you'), or rather, that 'they' are keen for 'you' to keep them informed.

There may not necessarily be any implication of 'keep a close watch on', which might in fact introduce an unwanted connotation.

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Note added at 18 minutes (2012-01-27 11:43:15 GMT)
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There's also an question over the translation of 'be interested in' here — this can have so many nuances in EN, and the obvious literal 'être intéressé par' is in fact relatively rarely the best solution. 's'intéresser à' may be more appropriate here, but once again, it depends on the precise overall context.

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